We designed a compound parabolic concentrator (CPC) with wings angled toward the east and west. Normally, solar collectors are straight, facing south, and the effective temperature is only achieved for a short period of time at midday. In the proposed design, the collector is divided into three parts, with the ends angled and tilted at different orientations. The objective was to increase the duration of the effective temperature period by capturing the maximum solar energy in the morning and afternoon without tracking by the collector. A simulation model was developed to evaluate the performance of the proposed CPC. The tilt and bending angles of the CPC wings were optimized for year-round operation in Tokyo, Japan. A 35° tilt for the south-facing central part of the CPC and a 45° tilt for the wings with 50° angles toward the east and west were found to be optimal. Analyses were conducted at these optimum settings with temperatures of 70, 80, and 90 °C as minimum requirements. The effective duration increased by up to 2 h in the winter and up to 2.53 h in the summer using the proposed CPC. The proposed CPC will improve the efficiency of solar-driven systems by providing useful heat for longer periods of time with the same collector length and without the need for tracking.