Citizens Advice Bureaux says the 51% increase means it is now Wales' biggest debt problem.
Council tax has increased by around 4% in the past year, and many cannot balance that with the cost of living.
The Welsh Local Government Association said it does its best to ensure the most vulnerable households are protected.
But the charity's report also found bailiffs knocked on the doors of 2,000 people last year in order to collect the tax.
A WLGA spokesman said: "In a period of such prolonged austerity, it comes as no surprise that the number of households reporting problems with paying their council tax has risen, on average bills are £160 less than in England.
"Council officers take an even-handed approach to enforcement."

Both sides have already qualified for the semi-finals the winners of Group A face Zamalek of Egypt while the runners-up will play South Africa's Mamelodi Sundowns.
Wydad know they need just a point to top the table and will take encouragement from their comfortable 2-0 win over Zesco in Morocco two months ago.
Coached by former Real Madrid manager and Liverpool striker John Toshack, Wydad top Group A with 10 points despite a mid-group crisis.
After wins over Asec Mimosas of the Ivory Coast and Zesco, the Moroccans only took one point from a possible six off struggling Al Ahly of Egypt.
Wydad then battled to translate dominance over Asec at home into goals until Congo Brazzaville-born Fabrice Ondama scored in the final minute to secure a 2-1 win.
That result, and Zesco holding record eight-time African champions Ahly 2-2 away, eliminated the Egyptian and Ivorian clubs.
Zesco have exceeded expectations by reaching the semi-finals although coach George Lwandamina remains worried about concentration lapses in defence.
"Our defence has a tendency to fall asleep after we score and this allows  opponents back into matches," said Lwandamina, who doubles as the caretaker  national coach.
What Zesco do boast are consistent goal  scorers with Idris Mbombo from the DR Congo scoring five in this Champions League campaign.
Clatous Chama and Kenyan Jesse Were have notched four each and John Ching'andu three.
Failing to reach the semi-finals cost Ahly coach and former Tottenham Hotspur manager Martin Jol his job amid safety concerns.
Assistant coach Ossama Orabi has taken charge for the meaningless midweek  match against 1998 champions ASEC at Stade Robert Champroux in Abidjan.
Another fixture where only pride is at stake involves already-eliminated  Enyimba of Nigeria and Sundowns in Port Harcourt.
Zamalek have a bye as Entente  Setif of Algeria were disqualified.
Over 6,000 people are struggling to pay council tax bills in Wales - double the number a year ago, says an advice body.
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Wydad Casablanca of Morocco travel to face Zesco United of Zambia on Wednesday to decide who tops Group A of the African Champions League.