Perovskite photodetectors (PPDs) based on all-inorganic charge transport layers (CTLs) exhibit promising future due to their remarkable sensing properties and improved stability against degradation. On the device level, however, their potential has not been explored theoretically. In this work, the MAPbI3 PD with all-inorganic CTLs, as a typical example, is numerically investigated using Silvaco TCAD software. To improve the performance of MAPbI3 PDs, the influence of thickness, doping density, defect density and carrier mobility of the absorber on photoelectric properties of the proposed PPD, including responsivity, detectivity and external quantum efficiency (EQE) is analyzed and optimized. After optimization, the optimal thickness and doping density of the absorber are determined to be 600 nm and 1014 cm−3, respectively. High quality absorber with defect density lower than 1015 cm−3 is required. Carrier mobility of no less than 10 cm2 V−1 s−1 is the key to efficient carrier transport and collection. Under these conditions, the maximum EQE is 89 % at 450 nm, the maximum responsivity value is 0.44 A/W at 675 nm, and the maximum detectivity is 7.5 × 1013 Jones at 675 nm. The knowledge developed from this work will promote the rational design of high-performance PPDs.