Sun sensors are commonly used attitude sensors because of their low cost, mass, volume, and power consumption. Analog Sun sensors (ANSS), which are smaller but usually less accurate than digital ones, are especially preferred for small satellite missions. One of the main reasons for the lesser accuracy of analog Sun sensors is being prone to external errors, most prominently the Earth's albedo. This study proposes an analog Sun sensor calibration method using the Deep Neural Network (DNN). The main contribution of the proposed algorithm is that it does not require any model for measurement correction. The method is tested with simulations and real data from an Earth-imaging spacecraft. Results show that the error in the Sun direction measurements, which can be as high as 10°, can be decreased to a level of 0.5° by using the DNN for calibration. Moreover, testing in different scenarios verifies that the DNN can correct the measurements for periods as long as 7 days without requiring excessive training periods, even when the spacecraft is not in the same flight configuration for which the DNN was trained.