In order to obtain a composite achromatic wave plate with adjustable retardation, temperature insensitivity, and achromatic bandwidth of 500 nm, a five-element composite achromatic quartz wave plate is designed based on particle swarm optimization. The total phase retardation can be adjusted by rotating the azimuth angle of the central wave plate. The results show that the total phase retardation is adjustable with the range of 90°-180° when the range of temperature and the achromatic wavelength is -20-80∘C and 750-1250 nm, respectively. The absolute value of the relative deviation of the maximum phase retardation is less than 3.6%, which meets the design requirements of the wave plate. The temperature insensitivity of the five-element wave plate is better than the three- and four-element wave plates. This method is of great reference value for designing this kind of composite achromatic wave plate.