In high perveance klystrons, violent variation of electron beam radius and electron transverse velocity is met with, and the energy exchange between kinetic electrons and gap field is a nonlinear process. For accurately describing these physical phenomena, we have put forward the corresponding physical model and further developed the 2.5-dimensional computation program LSP. Moreover, by use of this tool, we analyzed a practical S-band high peak-power klystron in detail. By comparing with the calculation results using 1-dimensional program and experimental data, we noticed that this poly-dimensional program can approach the real situation with higher precision.