Recently, there has been an increase in the demand for semiconductor detectors in the field of nuclear medicine imaging. The development of semiconductor detectors using materials such as CdTe that allowed for improved spatial resolution greatly advanced the field. However, the pinhole collimator that allows for high spatial resolution compromises the sensitivity due to the small size of the hole. An improvement in both sensitivity and spatial resolution may be achieved by using a pixelated parallel-hole collimator where the hole and pixel sizes are the same. The purpose of this study was to optimize the design of a detector and collimator system to achieve excellent resolution and high sensitivity for a SPECT detector based on a CdTe detector. We performed a simulation study of the PID 350 (Ajat Oy Ltd., Finland) CdTe detector by using a Geant4 Application for Tomographic Emission (GATE). In addition to the above-mentioned pixelated parallel-hole collimator, we also designed a hexagonal parallel-hole collimator with similar hole size, and we evaluated the sensitivity and spatial resolution of each to determine which set-up was optimal for the PID 350 CdTe detector. Our results indicated that the average sensitivity and spatial resolution were 33.48% and 10.97% higher for the pixelated parallel-hole collimator than for the hexagonal parallel-hole collimator, respectively. We resolved a diameter of 0.5 mm in hot-rod phantom images with the pixelated parallel-hole collimator at a distance of 2 cm. Based on our results, we recommend the pixelated parallel-hole collimator for improving the sensitivity and spatial resolution of SPECT systems with CdTe semiconductor detectors.