Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) have recently attracted significant research attention. However, in the transient processes of transmission lines, multiple traveling wave reflections pose challenges for standard models to achieve accurate solutions. This paper proposes a PINN-based computational method for lossless transmission line transient processes. Leveraging the characteristic of repeated wave reflections during transients, the method constructs multiple forward and backward sub-models. By incorporating boundary reflection functions to initialize model parameters, parallel computation of temporal transient processes is achieved. Case study results demonstrate that the proposed method achieves more than 50% reduction in Mean Absolute Error (MAE) and Mean Square Error (MSE) compared to the conventional PINNs. Furthermore, it accelerates convergence by 59.87% compared to the sequential computing model.