Direction of arrival (DOA) estimation is an important issue for radar and communication applications. Monopulse is widely used to obtain the DOA result by the complex ratio from the sigma and delta beams of the antenna. In the case of digital array systems, various methods based on the covariance matrix of the received signal have been proposed to obtain the DOA result. However, it is impractical for tracking radar scenarios, as the covariance matrix is not easy to obtain. Nevertheless, there is merely one target echo in the vicinity of the range cell as forecasted. Thus, the Maximum Likelihood Estimator (MLE) is a relatively good estimator for tracking radar, which has high accuracy and robustness. However, MLE is often very computationally resource-intensive, as it needs to search the whole steering vector set. In this letter, in order to utilize MLE effectively, we propose an algorithm to quickly search the steering vector set by the binary tree hierarchical matching method, which can significantly reduce the computational cost. Furthermore, the computational complexity and accuracy performance have been studied from both theoretical analysis and simulation perspectives.