We perform 3D smoothed particle hydrodynamics (SPH) simulations of gas accretion on to the seeds of binary stars to investigate their evolution until the mass of the seeds becomes 20 times larger than the initial mass. Taking into account dynamically evolving envelope with non-uniform distribution of gas density and angular momentum of accreting flow, our initial condition includes a seed binary and a surrounding gas envelope, modelling the phase of core collapse of gas cloud when the fragmentation has already occurred. Initial condition for envelope corresponds to the angular momentum distribution with j ∝ M, where j is the specific angular momentum of accreting gas at cylindrical radius π and M is mass contained inside π. We calculate dynamical evolution of binary seeds and envelope taking into account self-gravity. We find that binary separation increases with time by accretion of mass and angular momentum for our simulation setup. We also find that a circum-binary disc appears around binary seeds, which grows similarly with binary separation. We construct a semi-analytic model for binary separation. The angular momentum of accreted gas are the orbital angular momentum of binary seeds and the spin angular momentum of each binary star with circum-stellar disc. We find that binary separation is contributed only by the orbital angular momentum of binary seeds. Results of hydrodynamical calculations indicates the ratio of the orbital and spin angular momentum is apploximately 2 : 1. Binary separation from hydrodynamical calculation can be explained quantitatively by the semi-analytic model with using this ratio. Based on our semi-analytic model for binary separation, we analytically discuss the case with the angular momentum distribution j ∝ M^δ. It is found that binary separation keeps constant with binary mass when δ = 1/2 ≡ δorb, increases when δ > δorb, and decreases when δ < δorb.