The high performance method for analyzing the time evolution of the shielding current density in the high Tc superconductor (HTS) has been investigated. After discretized by using the finite element method and the backward Euler method, the initial-boundary-value problem of the governing equations of the shielding current density is transformed to the problem in which the nonlinear algebraic equations are solved at each time step. When the deaccelerated Newton method (DNM) is applied to the solution of the equations, a decrease in the relaxation factor will not always ensure the convergence of iterations. For this reason, the DNM is modified so that the residual norm may decrease monotonously with the iteration number. The modified method is called the adaptively deaccelerated Newton method (ADNM). Although the vector function is evaluated several times at each cycle in the ADNM, the CPU time required for the ADNM is diminished considerably as compared with that for the DNM. This result indicates that the ADNM is suitable for calculating the shielding current density. The numerical code for analyzing the shielding current density has been developed on the basis of the ADNM and, as an application of the code, the magnetic shielding performance of an axisymmetric HTS plate has been analyzed.