This research explores the effect of steam curing on the strength, durability and microstructure of concretes with and without mineral admixtures of fly ash (FA) and ground granulated blast-furnace slag powder (SL). Two types of C55 strength grade concretes (one was pure cement concrete, the other was a concrete made by replacing part of the cement with 12% FA and 18% SL) were prepared and their compressive strength, chloride diffusion coefficient and carbonation depth under standard and steam-curing conditions were measured and compared. The phase composition and microstructure of the concretes under the two curing conditions were tested by X-ray diffraction, scanning electron microscopy and mercury intrusion porosimetry. The results showed that, on the one hand, compared with standard curing, steam curing is beneficial to the early strength, but not conducive to the later strength development and chloride permeability resistance of both types of concretes. Furthermore, for the steam-cured concrete, the 28 days carbonation depth of the forming surface is higher than that of the bottom surface. In addition, steam curing can reduce the carbonisation resistance of pure cement concrete and improve the carbonisation resistance of concrete mixed with FA and SL. On the other hand, composite mineral admixtures of FA and SL reduce the early strength and the carbonisation resistance of concrete cured by standard curing, but improve the later strength, the carbonisation resistance and chloride permeability resistance of concrete cured by steam curing. FA and SL are thermally activated under steam curing and can react with the calcium hydroxide formed by cement hydration in the early stage, which produces a larger amount of secondary hydration products to improve the pore structure and interfacial microstructure of the concrete with FA and SL. In this way, the adverse effects of steam curing on later strength and durability of concrete are significantly restrained by composite mineral admixtures of FA and SL.