Abstract: The Iterative Adaptive Algorithm (IAA) is a super-resolution algorithm widely applied for high-accuracy direction of arrival (DOA) measurements in millimeter-wave radar systems. However, traditional IAA faces challenges such as algorithmic complexity and computational delays, rendering it unsuitable for real-time applications. Additionally, to mitigate angle estimation errors caused by mismatches between the source locations and the grid dictionary, grid refinement is commonly employed, further exacerbating the slow computational performance of the IAA. To address these issues, this paper proposes a Fast Iterative Adaptive Algorithm (FIAA). The FIAA utilizes a hierarchical grid refinement approach to iteratively estimate source angles. Initially, a coarse grid is applied over the entire spatial domain, identifying potential areas of the actual source locations using IAA. Subsequently, in these identified regions, a refined grid division is applied, and the signal direction matrix is updated. Finally, the IAA, incorporating a regularized covariance matrix, is utilized to achieve high-accuracy angle measurements. Experimental results show that FIAA effectively avoids scanning and computations in non-signal regions, reducing computational time to as little as 4% of the IAA, while maintaining comparable accuracy when the signal-to-noise ratio (SNR) exceeds 0dB. This approach is well-suited for high real-time and high-accuracy millimeter-wave radar DOA measurement scenarios.