This paper proposes the system design of a weighted-pendulum-type electromagnetic generator for harvesting energy from a rotating wheel. Different from the traditional energy-harvesting device, the natural frequency of the suitable weighted pendulum, which oscillates due to periodic change of the tangential component of gravitational force, can match up with the rotational frequency of the wheel at any speed. In addition, the pendulum oscillates at a large angle and angular velocity so as to generate a large amount of power. The physical model of the pendulum was first constructed and the equation of motion was then derived via the Lagrange method. Then, the models of power generation were derived by using Faraday's law of induction and the Lorentz force law. The nonlinear dynamic behaviors were discussed considering the characteristic length, variable electromagnetic damping, and wheel rotation speed. Finally, an experimental rig was constructed to verify the correctness of numerical results. The suitable weighted pendulum combined with coils and magnets has demonstrated the power generation of several hundred micro-Watts in the experiment.