In this work, inward solidification process of a spherical capsule subjected to a periodic boundary condition is numerically studied. The temperature transforming technique is utilized to solve the 1D phase change model and an in-house model developed in C++. The interface position and the transient temperature profiles are evaluated with respect to the different oscillation amplitudes and oscillation frequencies of the periodically oscillating surface temperature. The results demonstrate that in the situation where the amplitude is 30, the elapsed time for total solidification is dropped by 23.7% compared to the case without oscillation. It is also found that there is a 21.8% reduction in the time for total solidification when the frequency is changed from ω=π/64 to ω=0.