Because a scanning radar system works as a noncoherent sensor, it is suitable for any geometry situation, and it has significant and extensive applications, such as surveillance, autonomous landing of aircraft, navigation, and guidance. After the pulse compression technique of improving range resolution was presented, angular resolution became crucial for a scanning radar system. In this paper, a scheme of angular superresolution based on maximum a posteriori (MAP) framework is proposed. First, the received signal in azimuth is modeled as a mathematical convolution of the antenna pattern and the targets' scattering. Then, the principle of the angular superresolution algorithm, superresolution performance analysis, and computational implementation are presented. The algorithm can endure more significant disturbance of noise than conventional approaches. Simulation validates that the method can improve the radar angular resolution at least four times, even when the signal-to-noise ratio (SNR) is 10 dB. Furthermore, real data processing has proved the effectiveness of the proposed method.