The service, which resolves disputes between consumers and financial businesses, said many of the complaints about annuities could have been avoided if the pension firm had made more of an effort to explain "in plain English" exactly what an annuity is.
Common complaints were from people who bought a deal that turned out not to be suitable or were unaware they could not go back on their decision.
About three-fifths of people stick with their current pension provider when buying an annuity, but on average the benefit of switching equates to someone having saved an extra £1500 into their pension before they retired.
The Financial Ombudsman Service receives about 50 complaints a month about annuities and upholds about one-third of them. Complaint levels have remained steady in recent years, but the service said recent publicity about annuities could prompt an increase.
Many complaints brought to the ombudsman revolve around people saying their annuity was unsuitable, perhaps because their ill health was not taken into account or benefits for their partner were not included.
Otto Thoresen, director general of the Association of British Insurers, said: "We are finalising a new package of measures to enable people to engage and to shop around for better deals."