Abstract: A 2.5-Dimensional (2.5D) Particle-In-Cell (PIC) model is developed to study complicated nonlinear beam-wave interaction in the high-power klystron. Firstly, the particle charge and the beam current are properly assigned onto the grid based on the concept of PIC simulation. Secondly, the Finite-Difference-Time-Domain (FDTD) method is introduced to solve Maxwells equations so that the space charge of the electron beam can be accurately described. Thirdly, the port-approximation method is employed to simulate high-frequency cavity fields. Finally, the Lorentz equation is solved to further advance particle motion. The FDTD method and the port-approximation idea are combined for the first time in this model, which is more accurate than the traditional 1D nonlinear model, and, at the same time, is more efficient than the full 3D PIC method. The first domestic 2.5D particle-in-cell code, KLY2D, is developed based on this model. And an S-band 50MW high peak-power klystron is simulated using this code. The consistency between the theoretical results and the experimental results indicates the reliability of the theoretical model and the simulation code, which is of importance for further promoting the design and the development of high power klystrons.