Solid propellant rocket design for air-to-air missiles is the subject of this study. The most important design objective for an air-to-air missile is known to be maneuverability. It is known that there are many design parameters that affect maneuverability, but it is accepted in this study that maneuverability is a parameter related to the propulsion system of the missile, namely the thrust-to-weight ratio. Other design objectives are range and Mach number of flight. The cigarette type fuel core design was chosen for this study. Fuel rod diameter, fuel rod length and combustion chamber pressure were determined as the design parameters that will be effective in achieving these design objectives. The composite fuel type design was deemed appropriate to achieve the design objectives. PBAN/AP/AL, CTPB/AP/AL and HTPB/AP/AL fuel types were determined as design options. Determining the design parameters in line with the design objectives is carried out in this study. For this purpose, the change of design objectives depending on the design parameters is expressed graphically. The thrust-to-weight ratio is taken as the primary design objective and Mach number and range are taken as the lower priority design objectives. An optimization study was carried out to determine the design parameters that will achieve the design objectives. Meta-heuristic algorithms were selected as the optimization method. To determine the speed design objective, the drag model is obtained from the literature. Depending on this model, the flight Mach number is determined. Rocket materials in the literature are identified and tabulated. Fuel type and material selection are made based on the optimization results in line with the design objectives. Design choices and design parameters are determined by optimization method and conceptual design of solid fuel rocket for air-to-air missile is realized. In line with the studies, a missile with a maximum speed of Mach 4.6 and a range of 12.68 kilometers is designed. The thrust-to-weight ratio of the optimum designed missile is obtained above 16.