Large single-grain bulk high-temperature superconducting materials can trap high magnetic fields in comparison with conventional permanent magnets, making them ideal candidates to develop more compact and efficient devices, such as actuators, magnetic levitation systems, flywheel energy storage systems and electric machines. However, macro-segregation of Y-211 inclusions in melt processed Y–Ba–Cu–O (YBCO) limits the macroscopic critical current density Jc of such bulk superconductors, and hence, the potential trapped field. Recently, a new fabrication technique with graded precursor powders has been developed, which results in a more uniform distribution of Y-211 particles, in order to further improve the superconducting properties of such materials. In order to develop this graded fabrication technique further, a 3D finite-element numerical simulation based on the H-formulation is performed in this paper. The trapped field characteristics of a graded YBCO sample magnetized by the field cooling method are simulated to validate the model, and the simulation results are consistent with the experimental measurements. In addition, the influence of the graded technique and various graded Jc distributions for pulsed field magnetization, recognized widely as a practical route for magnetizing samples in bulk superconductor applications, is also investigated, with respect to the trapped field and temperature profiles of graded samples. This modelling framework provides a new technique for assessing the performance of various sizes and geometries of graded bulk superconductors, and by adjusting the Y-211, and hence Jc, distribution, samples can be fabricated based on this concept to provide application-specific trapped field profiles, such as the generation of either a high magnetic field gradient or a high level of uniformity for the traditionally conical, trapped field profile.