Connection with haunch is a new type of rigid connection. Single and cyclic load test is modeled using the program ANSYS. The result under different axial-compression ratio including hysteretic curve, the energy dissipation coefficient, and the plastic angle on beam ending is ascertained. The hysteretic curve under the ratio 0.3-0.6 is stable, and shows better plastic rotation ability. It exists a limit that axial-compression ratio has an effect on the connection with haunch, the model in this paper is 0.6. With hunch, the node can not only make the relocation of the plastic angle occur, but also increase yield stiffness, ultimate load, energy dissipation coefficient, linear displacement ductility coefficient and the plastic angle of beam end.