In a multiple-input multiple-output (MIMO) radar system, binary phase-shift keying (BPSK) modulation is widely used to separate signals transmitted from multiple transmit (Tx) antennas. However, when the BPSK modulation is applied to the frequency-modulated continuous-wave (FMCW) radar system, there is an occurrence of Doppler-angle ambiguity due to the properties of the modulation scheme. In other words, the maximum detectable velocity is reduced in proportion to the number of Tx antennas, and the angle estimation performance can be degraded when a moving target induces a Doppler phase shift. Therefore, in this paper, we propose a method for solving the Doppler-angle ambiguity in the BPSK-MIMO FMCW radar system. The proposed method involves comparing and arranging the phases of signals corresponding to the same target in the range-velocity detection results. By arranging the phases to form an arithmetic sequence, the signals from each Tx antenna can be distinguished and the unambiguous velocity and angle of the target can be estimated. In addition, by using a general phase-shift keying (PSK) modulation scheme, the proposed method can be applied to an arbitrary MIMO system regardless of the number of Tx antennas.