The Grammy award-winning artist said in a statement that he was choosing to "make a political stand".
He said reports of summary executions in the Philippines were "unacceptable to anyone who loves the rule of law".
President Rodrigo Duterte has vowed to eradicate drugs and urged citizens to kill dealers who resist arrest.
He was elected in May. In his previous role as mayor of Davao city, Mr Duterte built a reputation for blunt speaking and supporting the extrajudicial killings of suspected criminals.
James Taylor, 68, was scheduled to have played in the capital Manila next February.
"I don't think of my music as being particularly political but sometimes one is called upon to make a political stand," he said in a Facebook post.
"For a sovereign nation to prosecute and punish, under the law, those responsible for the illegal trade in drugs is, of course, understandable, even commendable; but recent reports from the Philippines... are deeply concerning and unacceptable to anyone who loves the rule of law."
Fans reacted with disappointment, but many praised the singer for his "integrity in adopting a principled stand".
"Thank you for your stand. I will miss seeing you perform but it's a small price to pay for standing up for one's principles," said Allan Victorino.
Another Facebook user Patricia Lyons, said: "We all need to take a stand, speak out and act on our truth."
But supporters of President Duterte criticised Taylor's "boycott" of their country.
"It's not our loss if he decided to cancel the Manila leg of his tour, it's his. James Taylor has missed the opportunity to perform before thousands of Filipinos, given the fact that he's now in the twilight of his career," said Wendell Sotto.
"Only fans will benefit from James Taylor's concert but good governance will benefit our entire nation," said Rendell Bata.

Up to 1,500 staff could be axed by 2017 due to a funding gap of almost Â£70m.
Mr Mallon said services would be closed and multimillion-pound projects reviewed in an attempt to stop the town "fraying at the edges".
The government said Middlesbrough received more funding than the national average and it should cut wastage.
Mr Mallon outlined the financial situation to councillors at a meeting on Wednesday and said he hoped action taken would "reduce substantially" the number of potential job cuts, but the loss of about 1,000 posts was "the best case scenario".
He said it was a "real shame" staff would be made redundant but insisted the council was "duty bound" to cut spending.
The council has just over 2,500 full-time staff, excluding those in schools.
More than Â£32m of the required savings are necessary due to changes in government funding and the authority is facing an increased demand on care services, Mr Mallon said.
"By 2018 or 2019, 75% of the council's budget will be spent on helping children and the elderly.
"The temperature has been rising for a long time and it's still rising."
Ahead of the meeting, Labour group leader Charlie Rooney said the town was being "devastated" by government cuts.
Conservative group leader Chris Hobson called on the authority to "start doing things differently".
"We've got to start running this council as a business," she said. "We've got to start bringing money in ourselves and thinking about how we can do that."
Mr Mallon will announce a list of specific budget proposals next month.
US singer James Taylor has cancelled an upcoming concert in the Philippines over reports of extrajudicial killings in the country's war on drugs.
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The loss of 1,000 jobs at Middlesbrough Council over the next three years is the "best case scenario", mayor Ray Mallon has said.