We extended the current density convolution finite-difference time-domain (JEC-FDTD) method to plasma photonic crystals using the Crank-Nicolson -difference scheme and derived the one-dimensional JEC-Crank-Nicolson (CN)-FDTD iterative equation of plasma photonic crystals. The method eliminated the Courant-Friedrich-Levy (CFL) stability constraint and became completely unconditional stable form. The incomplete Cholesky conjugate gradient (ICCG) algorithm is proposed to solve the equation with a large sparse matrix in the CN-FDTD method as the ICCG method improves the speed of convergence, enhances stability, and reduces memory consumption. The JEC-CN-FDTD method is applied to study the characteristics of time domain and frequency domain in the plasma photonic crystal objects. The high accuracy and efficiency of the JEC-CN-FDTD method are confirmed by computing the characteristic parameters of plasma photonic crystals under different conditions such as the electric field distribution of electromagnetic wave, reflection coefficients, and transmission coefficients. Simulation study showed that the algorithm performed stably and could reduce memory consumption and facilitate computer programming.