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Based on the equivalent circuit of a power transformer, considering both the nonlinear magnetizing characteristic of an iron-core and the nonlinear resistance of a superconducting secondary winding (V-I characteristic), the simulation of a magnetic shield type high Tc superconducting FCL was carried out by Simulink module of Matlab software. The transient response, especially the primary short circuit current is obtained. The influence of the saturation of an iron-core, and the specified structure of the magnetic circuit are analyzed. Based on the simulation, an improved magnetic shield type HTS FCL, a cross section adjustable power transformer with a multi-turn superconducting secondary winding is proposed. Its advantages include stable apparent impedance during the occurrence of a fault, shorter recovery time and lower voluminal energy dissipation during controlled S-N transition.