The magnetic phase diagram of rare-earth perovskite compound, GdScO3, has been investigated by magnetization andheat capacity. The system undergoes an antiferromagnetic phase transition at TN=2.6 K, with an easy axis of magnetization along the a axis. The magnetization measurements show that it exists a spin-flop transition around 0.3 T for the applied field along the a axis. The critical magnetic field for the antiferromagnetic-to-paramagnetic transition is near 3.2 T when temperature approaches zero. By scaling susceptibilities, we presume this point (B=3.2 T, T =0 K) might be a field-induced quantum critical point and the magnetic critical fluctuations can even be felt above TN.