Napier's apprenticeship with his father lasted for five years, after which time he moved to Edinburgh and worked for Robert Stevenson, builder of the Bell Rock Lighthouse.
In 1827, Napier had the unique distinction of having built the engines of both of the two fastest ships to compete in the Northern Yacht Club's August Regatta, namely the paddle steamers Clarence and Helensburgh.
This earned him a reputation as a shipbuilder, which furthered his career, as did his co-operation on hull design with Thomas Assheton Smith, for whom he built the Menai (400 tons and 120 hp) followed by several more steam yachts.
In 1838, Napier was contracted by the Admiralty to produce 280 NHP engines for two of their ships, the first class paddle steamer sloops Stromboli and Vesuvius; but after that, orders ceased.
Together with Cunard, James Donaldson, Sir George Burns, and David MacIver, he co-founded the British and North American Royal Mail Steam Packet Company.
It seems that Napier could be considered responsible for the livery of the Cunard funnels, since the vermilion colour and black hoops were already used on earlier Napier-engined ships, as evidenced by the shipbuilder's model of P.S.
In 1841 he expanded his company to include an iron shipbuilding yard in Govan and the Parkhead Forge Steelworks, and in 1843 they produced their first ship, the Vanguard.