The novel power-cycling variable transmission (PCVT) has special speed regulation characteristics, and its gearshift process is accompanied by sudden change of speed ratio and change of system efficiency, which affect the shift quality. In order to propose an effective shift control strategies, a dynamic model of shifting process is established based on the analysis of PCVT's working principle and speed regulation characteristics. According to the shifting mechanism of PCVT, the shifting process is divided into four stages, and the dynamic equation is established in stages. Based on the PCVT shift control requirements, the clutch and engine controller are designed in stages. For the torque phase, a finite time linear quadratic regulator is used to determine the optimal clutch engagement and disengagement speed, with the jerk and friction work as optimization indices. For the inertia phase, the fuzzy compensation controllers of the clutch and the engine are designed respectively under the comprehensive consideration of the factors such as the speed ratio of torque converter and the system efficiency. Simulation results show that the proposed shift control strategy can achieve smooth shift and meet the control requirements well.