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The series resonant induction heating process, with phase-lock loop by frequency adjustment and power regulation function by phase-shift, has strong nonlinearity and coupling. After analyzing the relationship between inverter frequency, output power, phase-lock angle and phase-shift angle, a compound control scheme for the phase-lock and phase-shift process of induction heating is proposed based on frequency domain separation principle. The heating control process is decomposed into the fast-slow subsystems, and the phase-lock controller and the phase-shift controllers with robust stability are designed separately. The coordination control problem between phase-lock control by frequency adjustment and power regulation by phase-shift is solved. The compound control scheme is applied to the supersonic frequency series resonant induction power supply of 20kW/40A. It is indicated that the safety of power switch devices in the inverter process is ensured, and the efficiency of power is improved. And the control scheme not only ensures the flexibility of power regulation, but also realizes the impedance self-matching of power supply.