Converting persistent and renewable wave energy into electricity has been a research focus in recent years. The oscillating-body wave energy converter (WEC) is a promising approach, especially for offshore areas. However, conventional oscillating-body WECs with linear power take-off (PTO) systems are less efficient under off-resonance conditions and have a narrow power capture bandwidth, which has inhibited the commercial application of wave energy. In order to enhance the power capture performance, this study examined oscillating-body WECs with three new types of PTO systems: bistable impulsive PTO, coupled linear PTO, and coupled bistable PTO. Governing equations for the heave motion of a WEC were established based on the linear potential theory by coupling the buoy and PTO systems and were numerically calculated with the fourth-order Runge–Kutta method. The influence of PTO parameters such as the spring constant, stable equilibrium position, and mass ratio on the power capture ratio was investigated. The differences among the WECs with different PTOs were analysed to determine the optimum device. Compared with the linear PTO system, the WEC with the bistable impulse PTO system enhanced the power capture ratio for low-frequency regular waves, and WECs with coupled linear or coupled bistable PTO systems increased the power capture ratio for low-frequency regular waves and expanded the power capture spectrum bandwidth when proper PTO parameters were applied.