To study the nonlinear beam-wave interaction for sheet beam klystron (SBK), a 2-D simulation code of SBK2D, based on the 2-D rod macroparticle model, has been designed and realized thoroughly in this paper. In our physical model, the sheet beam is simulated by a series of rods with nonzero thickness and length in y and z directions, respectively (y is the direction of sheet beam's narrow dimension, and z is the direction of beam motion). Then, the space-charge forces between the rod macroparticles are calculated by Green's functions approach, and the port-approximation methods are employed to simulate high-frequency fields for each cavity. Furthermore, the relativistic Lorentz motion equation is solved to obtain the parameters for further macroparticle motion, and the specific criterions are introduced to deal with the sheet beam interception problem by the tunnel and cavities. To verify our simulation code, an eight-cavity W-band SBK has been designed, calculated, and analyzed by SBK2D in detail. The good consistency between SBK2D and 3-dimensional Particle in Cell (3-D PIC) program indicates the reliability of the physical model and simulation code for our program. In addition, the calculation time of SBK2D is only about 1% of that of the 3-D PIC, which makes it more feasible and efficient to calculate and optimize the initial physical parameters for the design of complicated SBK.