It reported Â£740m in annual adjusted operating profit before transformation costs, up 6% from a year earlier.
Revenues in the year to 29 March were barely changed at Â£9.4bn.
UK parcel volumes grew by 3%, although revenues from its parcels business rose by just 1%. Letter volumes fell by 4%, with revenues from letters down 1%.
The company expects this year to follow a similar pattern to last year, with strength coming in the second half.
Royal Mail chief executive Moya Greene said: "Our trading environment remains challenging.
"At this early stage of the financial year trading is in line with our expectations, but as in previous years our performance will be weighted to the second half and will be dependent on our important Christmas period."
Competition in the UK parcels and letters market is fierce, the company said.
Royal Mail said it expects Amazon's parcel delivery service will limit the rate of growth in its parcels business in the short term.
The online retailer is increasing the number of parcels it delivers using its own network.
That is contributing to the stiff competition Royal Mail faces.
But the sector is shifting: one of Royal Mail's rivals, Whistl, formerly known as TNT UK, ceased its letters service earlier this month.
Whistl was Royal Mail's main competitor in the market for last mile delivery, a term which refers to the final leg of a delivery route.
Ian Senior, independent postal expert, told the BBC's Today programme: "Royal Mail must be smacking its lips with joy that Whistl has withdrawn from trying to do 'final mile' delivery."
Mr Senior also said he thought Royal Mail's results were good: "They're at the upper end of what people were expecting."
Richard Hunter, Head of Equities at Hargreaves Lansdown Stockbrokers, noted that even with Whistl's removal from the market, competition was still tough.
He said: "Royal Mail has posted numbers which indicate measured progress in a treacherous environment."
Shares in Royal Mail were 1.5p lower at 498.40p by midday.
Royal Mail has reported an increase in full-year profits, with cost cuts helping the company in a "challenging" market.