Cavity internal electromagnetic pulse (IEMP) is generated by the irradiation of X-rays on cavities, such as spacecrafts. It would disturb the normal operation of electrical systems inside spacecrafts and further affect their survival. In this paper, we present a 3D parallel full electromagnetic particle-in-cell (PIC) method for simulating cavity IEMP responses. In the proposed method, the finite difference time domain (FDTD) method and the PIC method are used to solve the coupling between the formation of transient electromagnetic fields and the movement of particles; the effective current distribution method is adopted to compute the source of electromagnetic fields, which is the current density. The proposed method is coded based on JASMIN, so it supports massively parallel computing and could be used to simulate cavity IEMP responses with hundreds of millions mesh cells and hundreds of millions particles. In the end, the proposed method is applied to compute the IEMP responses of a cylinder irradiated by pulsed X-rays. The results agree well with those from literature, verifying the accuracy of the proposed method.