Mark Glasswell, 34, of Simmons Way, Gipton, bludgeoned one of his victims with a hammer and also set fire to a house with a 78-year-old woman inside.
He pleaded guilty to a number of charges and was jailed for life with a minimum term of six years.
Police described Glasswell as a "despicable individual".
West Yorkshire Police said his crime spree began on 8 September last year by robbing a clothes store on Vicar Lane after threatening a store assistant.
Two days later he went to the home of an 86-year-old woman on Pendas Walk where he hit her several times over the head with a hammer.
The victim suffered two skull fractures and a broken eye socket and had to have 50 stitches in her head.
The following day he ripped the handbag off the shoulder of an 82-year-old woman walking on Beckett Street.
Later that day he returned to Leeds where he went into a shop and threatened a staff member with a plastic handgun.
Police said Glasswell's final offence took place in the early hours of 12 September when 78-year-old Jean Lord was woken in her home by Glasswell, who was stood in the door of her bedroom and threatened her with the same replica firearm.
He dragged her downstairs and threatened to pour boiling water over her head before making off with jewellery and a DVD player.
Leaving Mrs Lord injured on the living-room floor, Glasswell then started two fires as he left, one in front of the main door and the other in front of a desk containing all the keys to the house.
Mrs Lord managed to escape and raise the alarm with a neighbour.
Glasswell admitted aggravated burglary, assault, theft, robbery, attempted robbery, false imprisonment and arson with intent to endanger life.

South West Trains said the line between Eastleigh and Fareham via Botley had been shut because of flooding.
The B3354 Winchester Road in Botley was also closed after two trees came down, one on to a van - the driver was taken to hospital with a fractured sternum.
Residents in Bishops Waltham and Botley have been warned to prepare for flooding, with more rainfall forecast.
A flood warning has been issued by the The Environment Agency (EA) for the Upper River Hamble area including Durley Mill and Botley Mills.
The (EA) said more than 50mm of rain had been recorded at Bishops Waltham overnight.
Police have urged drivers not to risk driving through floodwater.

The club wants to develop the former Twelve Oaks Golf Club in Highworth into a training ground and offices.
The Robins' chairman, Lee Power said: "Nigel Eady left a significant sum of money in his will to be invested for the benefit of STFC and the community."
Currently the club leases its stadium from Swindon Borough Council.
Nigel Eady was a lifelong supporter of Swindon Town and bequeathed the undisclosed sum from his will.
DBS Consulting is involved in the project and the ongoing talks between the trust and football club.
Managing director, Les Durrant, said: "Discussions have been going on between the Nigel Eady Trust and Swindon Town because the trust want to invest in it, not just for the football club but also for the wider community.
"The discussions have been around the trust taking ownership of the site and the facilities being developed for the football club to be used."
The former golf club was bought by Mr Power a year go but as yet it has no planning permission.
The hope is to create a new gym, treatment rooms, lecture rooms, grass training pitches and a floodlit 4G artificial surface pitch.
On Wednesday evening, the club met the town councillors to talk through the project.
Mr Power added: "We are working closely with the Nigel Eady Trust and the local community.
"We will be developing our proposals in greater detail after further consultation with local people and clubs/organisations over the next few weeks.
"We want this new training centre and pitch facilities to be of benefit to the local clubs as well as Swindon Town."
The aim is to develop the site over the 24 months.
A man who carried out a five day crime spree across Leeds including attacking two elderly women in their homes has been jailed for life.
[NEXT_CONCEPT]
Heavy downpours have hit train services and left roads in parts of Hampshire impassable.
[NEXT_CONCEPT]
Swindon Town FC hopes to develop new training facilities with the help of money from a trust set up by a former supporter.