In pulsed field magnetization (PFM), the phenomenon of flux jump is capable of driving magnetic flux vortexes into GdBCO superconducting bulk center to aid full magnetization. Varieties of homogeneous critical current density (Jc) models have been implemented to reproduce flux jumps, but simulated multi-physical responses differ from experimental observations. This paper proposes a modified Jc model to consider r-z plane Jc inhomogeneity and simulates flux jumps under experimental conditions by solving a 2D axisymmetric electromagnetic-thermal coupled model. A numerical treatment is developed to reflect the break of shielding current during flux jumps. The accuracy of our model is verified by comparisons of the calculation results of trapped magnetic fields (BT) and the PFM and field cooling (FC) experimental results. On this basis, we investigate the improvement of inhomogeneous Jc model and obtain the multi-physical responses which have better agreement with the experimental results compared to homogeneous Jc model. Moreover, to further test the ability of the inhomogeneous Jc model to predict anisotropy of spatially magnetic field distribution, the simulated BT profiles in top and bottom surfaces of HTS bulk at 77 K are compared to the experiments. This study may provide a new approach for modelling the inhomogeneity of Jc characteristics and a useful analysis tool for industrial devices using high-temperature superconductor (HTS) bulk magnets.