The application of convolutional neural network (CNN) in reconstructing the position of charged particles incident on the plastic scintillator detector (PSD) is presented. We first simulated the trapezoid PSD, similar to the design used by the HERD experiment in 2023 beam test, using GEANT4 toolkit. The number of photons (to emulate the amplitude measurement) is utilized as an input to the CNN to reconstruct the muon incident position, thereby achieving a position resolution of \(\sim \) 1.38 cm along the bar. To evaluate the capability of measuring two-dimensional position, we simulated a square PSD with a dimension of 10 cm \(\times \) 10 cm and nine evenly distributed SiPMs. The position resolutions in both directions are \(\sim \) 0.89 cm with only amplitude information, \(\sim \) 0.91 cm with only time information, and \(\sim \) 0.68 cm with both amplitude and time information. Additionally, waveform conversion is performed and the calculated integral amplitude and time-of-arrival are used for training, the result is \(\sim \) 0.71 cm in both directions. The position resolution can be further improved according to the requirement of specific experiment by reducing the spacing between SiPMs.