To analyze the time-varying plasma, a modified finite-difference time-domain (LTJEC-FDTD) algorithm is derived. By using Laplace transform and inverse Laplace transform, we can deduce the FDTD iteration expression for calculating 3D time-varying problem from Maxwell equation and plasma constitutive equation. The iteration expression is proven to be correct by mode-coupling theory, while the correctness of the relevant boundary is tested by calculating the radar cross-section (RCS) of plasma sphere. So, the method is suitable to the calculation of time-varying plasma. Then, the RCS of complex time-varying plasma object is also analyzed.