Considering the secondary oscillation period when a Virtual Synchronous Generator (VSG) is applied to microgrid frequency modulation, a double threshold-full adaptive frequency control strategy is proposed. The control strategy combines the adaptive model and the characteristics of negative inertia, establishes inertia of the new function model, and weakens the effect of damping. It simplifies the control structure while eliminating the secondary oscillation period of the frequency transient process. In order to solve the problem that the existing single control strategy is not suitable for the black start of a microgrid, a zero start and boost link is introduced on the premise of not affecting the start speed of the microgrid. This extends the application scope of this control strategy to the black start process of a microgrid. Simulation and experiment validate the correctness and effectiveness of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51974151) and Fund Program of Liaoning Provincial Key Laboratory (No. LJZ003).