The invention relates to a double active clamp quasi-resonant BOOST full bridge topology and a control method. The topology comprises an H bridge composed of four active switch tubes from S1 to S4. The input end of the H bridge is connected in parallel with a clamp branch formed by connecting a clamp switch tube Sax and a clamp capacitor Ca in series, and a resonance branch formed by connecting aresonant switch tube Sr and a resonant capacitor Cres in series. One end of a boost inductor L is connected with the input end of the clamp branch, and the other end is connected with an external power supply. The output end of the H bridge is connected with the primary side of a transformer through a resonant inductor Lr. The primary side of the transformer is connected in parallel with a magnetic inductor. The secondary side of the transformer is connected with the input end of a rectifier bridge. The output end of the rectifier bridge is connected in parallel with an output rectifying capacitor Co. According to the invention, soft switching of an active power semiconductor device of the whole circuit in the processes of turning on and off is realized; the loss of a converter is reduced;and the efficiency of the converter is improved.