In this work, we systematically conduct parametric studies revealing the sensitivity of the hole injection on the hole accelerator (a hole accelerator is made of the polarization mismatched p-electron blocking layer (EBL)/p-GaN/p-AlxGa1-xN heterojunction) with different designs, including the AlN composition in the p-AlxGa1-xN layer, and the thickness for the p-GaN layer and the p-AlxGa1-xN layer. According to our findings, the energy that the holes obtain does not monotonically increase as the AlN incorporation in the p-AlxGa1-xN layer increases. Meanwhile, with p-GaN layer or p-AlxGa1-xN layer thickening, the energy that the holes gain increases and then reaches a saturation level. Thus, the hole injection efficiency and the device efficiency are very sensitive to the p-EBL/p-GaN/p-AlxGa1-xN design, and the hole accelerator can effectively increase the hole injection if properly designed.