Based on the classical grid theory and related regulations, a structure model of a fiber-wound composite gas cylinder was designed in this paper. Based on the design results, a finite element model of a fully wound composite cylinder of an aluminum alloy inner liner with a working pressure of 35 MPa was established based on the ABAQUS software, and its stress distribution under working pressure and minimum burst pressure was analyzed. According to engineering experience, the pressure tolerance of composite cylinders can be improved by proper autofrettage pressure before working pressure, so the influence of autofrettage pressure was analyzed in this paper. The optimum autofrettage pressure was selected by setting the autofrettage gradient, and damage analysis was carried out on the cylinder with nominal working pressure of 35 MPa based on the Hashin failure criterion. The results show the initial damage sequence: matrix stretching occurs before the fiber stretching, and the damage generally starts from the spiral-wound layer. The tensile damage first appears in the transition section between the head and the barrel body, and the damage of the spiral-wound layer develops from the inner layer of the wound layer to the outer layer, while the damage of the circumferentially wound layer develops from the outer layer to the inner layer.