A two-axis tracking solar concentrator system includes a sunlight concentrator, a Fresnel lens, a two-axis solar tracker, sunlight reflectors, an enclosure, a sunlight conversion device, and other components. The lens has very long focal length so that all concentrated sunlight will enter the sunlight conversion device through a small window. The elevation rotation axis goes through the focal point so that the sunlight conversion device will remain at the same horizontal level all the time. The concentrated sunlight makes it easy to achieve a needed temperature. The two-axis tracking design eliminates the need of frequent adjustment. An offset design permits having the sunlight conversion device under shade, so that people do not have to expose themselves to sunlight to do solar cooking. The enclosure significantly reduces the risk of burns and fires. It also makes it very easy to control the heating or cooking process.