We perform three-dimensional cosmological simulations to examine the growth of metal-free, Population III (Pop III) stars under radiative feedback. We begin our simulation at z= 100 and trace the evolution of gas and dark matter until the formation of the first minihalo. We then follow the collapse of the gas within the minihalo up to densities of n= 1012 cm−3, at which point we replace the high-density particles with a sink particle to represent the growing protostar. We model the effect of Lyman–Werner (LW) radiation emitted by the protostar, and employ a ray-tracing scheme to follow the growth of the surrounding H ii region over the next 5000 years. We find that a disc assembles around the first protostar, and that radiative feedback will not prevent further fragmentation of the disc to form multiple Pop III stars. Ionization of neutral hydrogen and photodissociation of H2 by LW radiation leads to heating of the dense gas to several thousand Kelvin, and this warm region expands outward at the gas sound speed. Once the extent of this warm region becomes equivalent to the size of the disc, the disc mass declines while the accretion rate on to the protostars is reduced by an order of magnitude. This occurs when the largest sink has grown to ∼20 M⊙ while the second sink has grown to ∼7 M⊙, and we estimate the main sink will approach an asymptotic value of 30 M⊙ by the time it reaches the main sequence. Our simulation thus indicates that the most likely outcome is a massive Pop III binary. However, we simulate only one minihalo, and the statistical variation between minihaloes may be substantial. If Pop III stars were typically unable to grow to more than a few tens of solar masses, this would have important consequences for the occurrence of pair-instability supernovae in the early Universe as well as the Pop III chemical signature in the oldest stars observable today.