A marching-on-in-time (MOT)-based nonconformal volume integral equation (VIE) is proposed to analyze the transient electromagnetic scattering from the inhomogeneous penetrable objects. The gradient–gradient operator is acted on the Green’s function to realize the nonconformal tetrahedral meshes discretization. Half Schaubert–Wilton–Glisson (SWG) basis functions are chosen for the trail and test spatial functions, meanwhile the piecewise polynomial Lagrange interpolation functions are applied for temporal expansion. In addition, the quasi-explicit scheme is introduced to accelerate the calculation of conventional implicit MOT system. Numerical results are given to demonstrate the flexibility and validity of the proposed scheme.