Titanium trisulphide (TiS3) has been widely used in the field of optoelectronics owing to its superb optical and electronic characteristics. In this work, a self-powered photodetector using bulk PbS/TiS3 p-n heterojunction is numerically investigated and analyzed by a Solar Cell Capacitance Simulator in one-Dimension (SCAPS-1D) software. The energy bands, electron-holes generation or recombination rate, current density-voltage (J-V), and spectral response properties have been investigated by SCAPS-1D. To improve the performance of photodetectors, the influence of thickness, shallow acceptor or donor density, and defect density are investigated. By optimization, the optimal thickness of the TiS3 layer and PbS layer are determined to be 2.5 μm and 700 nm, respectively. The density of the superior shallow acceptor (donor) is 1015 (1022) cm−3. High quality TiS3 film is required with the defect density of about 1014 cm−3. For the PbS layer, the maximum defect density is 1017 cm−3. As a result, the photodetector based on the heterojunction with optimal parameters exhibits a good photoresponse from 300 nm to 1300 nm. Under the air mass 1.5 global tilt (AM 1.5G) illuminations, the optimal short-circuit current reaches 35.57 mA/cm2 and the open circuit voltage is about 870 mV. The responsivity (R) and a detectivity (D*) of the simulated photodetector are 0.36 A W−1 and 3.9 × 1013 Jones, respectively. The simulation result provides a promising research direction to further broaden the TiS3-based optoelectronic device.