A problem about the calculation error of the classical Z-transformation finite difference time domain (Z-FDTD) method in the analysis of the transmission characteristics of electromagnetic wave and non-uniformly magnetized plasma is studied. A modified Z-transform finite difference time domain (MZ-FDTD) method is discussed to improve the applicability of the Z-FDTD method for non-uniformly magnetized plasmas. For the calculation error between MZ-FDTD and Z-FDTD, the calculation formula of the error is derived, and error analysis factor is introduced. The characteristics of the error affected by the spatial step size and the physical characteristics of non-uniformly magnetized plasma are compared and analysed. After sufficient error analysis and mesh parameter comparison, the advantages of MZ-FDTD are illustrated by analysing the propagation characteristics of electromagnetic wave in inhomogeneous magnetized plasma as the objective. The research results show that compared with the classical Z-FDTD, the numerical results obtained by MZ-FDTD method have higher calculation accuracy, lower running time and memory consumption. In addition, the analysis of electromagnetic wave transmission characteristics in non-uniform plasma also proves that compared with Z-FDTD, the numerical results obtained by MZ-FDTD method are relative stability, no matter whether it's in the low band. In the future, using MZ-FDTD method to study the problem of non-uniformly magnetized plasma will get better calculation results, and the error analysis method in this work will also play a helpful role in the application and optimization of some computational electro-magnetics in plasma.