A core–shell nanowire heterostructure is an important building block for nanowire-based optoelectronic devices. In this paper, the shape and composition evolution induced by adatom diffusion is investigated by constructing a growth model for alloy core–shell nanowire heterostructures, taking diffusion, adsorption, desorption and incorporation of adatoms into consideration. With moving boundaries accounting for sidewall growth, the transient diffusion equations are numerically solved by the finite element method. The adatom diffusions introduce the position-dependent and time-dependent adatom concentrations of components A and B. The newly grown alloy nanowire shell depends on the incorporation rates, resulting in both shape and composition evolution during growth. The results show that the morphology of nanowire shell strongly depends on the flux impingement angle. With the increase in this impingement angle, the position of the largest shell thickness on sidewall moves down to the bottom of nanowire and meanwhile, the contact angle between shell and substrate increases to an obtuse angle. Coupled with the shell shapes, the composition profiles are shown as non-uniform along both the nanowire and the shell growth directions, which can be attributed to the adatom diffusion of components A and B. The impacts of parameters on the shape and composition evolution are systematically investigated, including diffusion length, adatom lifetime and corresponding ratios between components. This kinetic model is expected to interpret the contribution of adatom diffusion in growing alloy group-IV and group III-V core–shell nanowire heterostructures.