Abstract: Recent advancements in proton accelerator technology have sparked growing research interest due to expanding applications in cancer therapy, industrial processing, and scientific investigations. The development of high-gradient radio frequency (RF) accelerating structures operating at GHz frequencies has enabled compact proton linacs with enhanced performance. While extensive design codes exist for standing wave structures, a notable gap remains in design code for travelling wave structures. This work presents a novel particle dynamics tracking (PDT) code capable of beam dynamics design for both standing wave and travelling wave accelerating structures based on unit cell electromagnetic field distribution. The benchmark against the commercial linac beam dynamics simulation code TraceWin demonstrates good agreement in energy gain and beam envelope. The code has been applied in the beam dynamics design of a 30~100 MeV low current backward travelling wave proton linac, which operates at RF frequency of 2.856 GHz and working at 5π/6 mode. The linac spans a total length of approximately 3 m, comprising 10 tanks and 10 permanent magnet quadrupoles. It operates with a 30 MV/m accelerating gradient, characterized by full transmission and low emittance growth.