In this paper, we consider the joint angle-range estimation in monostatic FDA-MIMO radar. The transmit subarrays are first utilized to expand the range ambiguity, and the maximum likelihood estimation (MLE) algorithm is first proposed to improve the estimation performance. The range ambiguity is a serious problem in monostatic FDA-MIMO radar, which can reduce the detection range of targets. To extend the unambiguous range, we propose to divide the transmitting array into subarrays. Then, within the unambiguous range, the maximum likelihood (ML) algorithm is proposed to estimate the angle and range with high accuracy and high resolution. In the ML algorithm, the joint angle-range estimation problem becomes a high-dimensional search problem; thus, it is computationally expensive. To reduce the computation load, the alternating projection ML (AP-ML) algorithm is proposed by transforming the high-dimensional search into a series of one-dimensional search iteratively. With the proposed AP-ML algorithm, the angle and range are automatically paired. Simulation results show that transmitting subarray can extend the range ambiguity of monostatic FDA-MIMO radar and obtain a lower cramer-rao low bound (CRLB) for range estimation. Moreover, the proposed AP-ML algorithm is superior over the traditional estimation algorithms in terms of the estimation accuracy and resolution.