Based on the dynamic equation of a direct-drive linear wave energy converter, a linearized and modified model including linearization of nonlinear parts and identification of parameters that are hard to measure is proposed. An equivalent sixth-order model is obtained using either a transfer-function or a state-space model. Based on the state-space model, a real-time identification of wave excitation force is proposed through the Kalman filter. The characteristics of power extraction are analyzed in detail in the frequency domain for the wave energy converter under real wave excitation, and furthermore, the optimal power extraction conditions are obtained. An optimal power control method in real time is proposed for a resonance operation between the ocean waves and the float by controlling the velocity of the linear generator. Simulation and experimental results demonstrate that the proposed method is valid, and capable of achieving a high power extraction efficiency.