  We perform three dimensional smoothed particle hydrodynamics (SPH)
simulations of gas accretion onto the seeds of binary stars to investigate
their short-term evolution. Our simulation setup is more realistic compared to
the previous works by taking into account of 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. We assume that the seed binary has no eccentricity and no
growth by gas accretion. The envelope is assumed to be an isothermal gas with
no self-gravity. We run multiple simulations with different values of initial
mass ratio $q_0$ (the ratio of secondary over primary mass) and gas
temperature, and find a critical value of $q_{\rm c} = 0.25$ which
distinguishes the later evolution of mass ratio $q$ as a function of time. If
$q_0$ >~ $q_{\rm c}$, the secondary seed grows faster and $q$ increases
monotonically towards unity. If $q_0$ <~ $q_{\rm c}$, on the other hand, the
primary seed grows faster and $q$ is lower than $q_0$ at the end of the
simulation. Based on our numerical results, we analytically calculate the
long-term evolution of the seed binary including the growth of binary by gas
accretion. We find that the seed binary with $q_0$ >~ $q_{\rm c}$ evolves
towards an equal-mass binary star, and that with $q_0$ <~ $q_{\rm c}$ evolves
to a binary with an extreme value of $q$. Binary separation is a monotonically
increasing function of time for any $q_0$, suggesting that the binary growth by
accretion does not lead to the formation of close binaries.
