A diagonal-cut type beam position monitor (BPM) has been developed for the High Intensity Heavy-Ion Accelerator Facility (HIAF) project at the Institute of Modern Physics. Compared with other types of BPMs, the diagonal-cut type BPM has almost perfect position linearity, i.e., no non-linear correction required, which is advantageous for beams that are transversally large and have a complex charge distribution. The key parameters for the diagonal-cut type BPM have been simulated and optimized in detail and systematically herein. It was found that the crosstalk is improved by ∼10 dB at 160 MHz by insertion of a separate ring between two horizontal or vertical electrodes of the BPM made of stainless steel with vacuum as a dielectric. Furthermore, the longitudinal and transverse numerical simulation to evaluate the beam impedance on the diagonal-cut type BPM has been performed. The results for the crosstalk, position sensitivity, and electrode capacitance to ground obtained from simulations and laboratory measurements agree well. The vacuum of the BPM prototype after baking out at 250 °C for 72 h is better than 1.0 × 10-11 mbar. The simulated and on-line measured BPM output signal magnitude results are consistent with each other. This diagonal-cut type BPM structure will be considered for application to the HIAF project as a priority.