The invention relates to a boost converter possessing a circuit of controlling a body of a boost output rectification transistor and a method. A first soft starting signal indicates operation of a boost rectifier in a loading phase, and a second soft starting signal indicates operation in a pulse driving phase after the loading phase. A rectifying transistor corresponds to the first soft starting circuit and is exited in loading-phase continuous time so as to form a rising output voltage. The rectifying transistor further corresponds to the second soft starting circuit and is repeatedly excited in the pulse driving phase so as to form a boost output voltage. In the loading phase, a first transistor coupled between a first conductive terminal and a body terminal of the rectifying transistor is excited, and a second transistor coupled between the body terminal and a second conductive terminal of the rectifying transistor is stopped. In the pulse driving phase, the first transistor is stopped, and the second transistor is excited.