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.