There were nearly 40,000 new complaints brought last year, up a "startling" 130% on the 17,000 the previous year, the Financial Ombudsman Service said.
In too many cases people have been left to struggle with debt, it said.
Short-term lender industry body the Consumer Finance Association (CFA) said most of the complaints dated back a number of years.
Complaint flood
Most of the complaints were made about affordability. Some customers took out 20 to 30 loans in a short space of time, either to pay off other outstanding loans or for household bills.
Many of the complaints came through claims management companies, the CFA said.
A CFA spokeswoman said: "These figures show a deeply disappointing increase, driven by a flood from claims management companies and we continue to see many a complaint that has no foundation.
"Now nearly nine in 10 of complaints to firms are generated by these companies. The complaints are often of poor quality."
She added that the lender has to pay the case fee regardless of who submits the complaint, and said some members had questioned the ombudsman's complaint figures.
Last calendar year the highest volume of complaints were made against QuikQuid owner Casheuronet.
'Will I be paid back?'
John from Stockton on Tees says he has had payday loans with "virtually every company out there", including ones that have gone into administration.
"I am in contact with the administrators by email who tell me I am owed thousands but if I receive anything it will be next year and a small percentage of what I am owed," he says.
"I have also come to an agreement with one lender who has agreed to refund me £350 without involving the financial ombudsman.
"The problem with all this though is that I was paying back these debts with all the inflated interest and charges for months.
"Now these loans no longer exist will I get these payments back?"
Overall, complaints about financial services shot up to a five-year high, with more than 388,000 new complaints made in the last financial year, a 14% increase on the previous year.
Caroline Wayman, chief ombudsman and chief executive of the Financial Ombudsman Service, said: "Too often we see that the interests of consumers are not hard-wired into financial services.
"This marks a five-year high in the number of complaints that consumers have brought to us, and the behaviour we've seen from some businesses is simply not good enough."
The Financial Ombudsman Service added that complaints about fraud and scams increased by more than 40% in 2018-2019, with more than 12,000 received.
Gareth Shaw of consumer group Which? said: "Bank transfer fraud is spiralling out of control, with people losing life-changing sums every day and then facing a gruelling battle to get their money back from the very banks that should be preventing them from falling victim in the first place."
Analysis: By Simon Gompertz, personal finance correspondent
Payday lenders say that they have faced a flood of spurious compensation claims, driven by commission-hungry claims management companies.
The lenders are furious that if the borrower appeals to the Financial Ombudsman Service they have to pay £550 per case whatever the outcome.
And since the collapse of Wonga, which fell into administration in August last year, the rush to complain has become even more urgent because of the fear that more firms will fail and the compensation will dry up.
But while the ombudsman agrees that the numbers of complaints are "startling", it has little sympathy for payday lenders which it says have left too many people struggling with debt.