Short-time dynamic behaviour of two-dimensional fully frustrated XY model near the Ising-like phase-transition temperature is studied with resistively shunted junction dynamics. The transition temperature Tc and the dynamic and static critical exponents z, 2β/v and v are estimated under both a periodic boundary condition (PBC) and a fluctuating twist boundary condition (FTBC) using the short-time dynamic scaling analysis. The results show that Tc, 2β/v and v are almost independent of the boundary conditions, whereas z depends on the boundary condition. The value of z = 2.18(5) of the PBC is roughly equal to that of the FFXY model with Monte Carlo dynamics under the PBC, while z = 2.05(4) of the FTBC is in agreement with that of the Coulomb gas model.