In this paper, diamond-based vertical p-n junction diodes with step edge termination are investigated using a Silvaco simulation (Version 5.0.10.R). Compared with the conventional p-n junction diode without termination, the step edge termination shows weak influences on the forward characteristics and helps to suppress the electric field crowding. However, the breakdown voltage of the diode with simple step edge termination is still lower than that of the ideal parallel-plane one. To further enhance the breakdown voltage, we combine a p-n junction-based junction termination extension on the step edge termination. After optimizing the structure parameters of the device, the depletion regions formed by the junction termination extension overlap with that of the p-n junction on the top mesa, resulting in a more uniform electric field distribution and higher device performance.