This paper proposes a range-Doppler imaging method based on FFT-MUSIC method for FMCW radar systems. With the growing significance of vehicle and human motion recognition in automotive radar, the accuracy of conventional deep learning network-based recognition methods is reduced because it depends only on distance, speed, and angle information provided by conventional radars. Therefore, various types of imaging radar methods have recently been proposed. Among them, the range-Doppler imaging algorithm is widely used. This algorithm can simultaneously analyze both distance and velocity characteristics of a vehicle or person. However, conventional range-Doppler imaging based on the FFT algorithm has limited resolution, which cannot obtain detailed information on the target. Although the FFT algorithm is widely used in many applications, its low-resolution characteristics can limit its ability to provide detailed information. In particular, improving velocity resolution often requires the extraction of a significant amount of data. To address this issue, a range-Doppler imaging method based on FFT-MUSIC is proposed in this paper. This technique has been simulated using Remcom's WaveFarer® software package. The proposed algorithm is effectively able to distinguish between two moving vehicles in several cases in which the ranges and velocities are too close to be resolved by conventional FFT methods. We can observe that the proposed algorithm enhances the velocity resolution by approximately twice as much as the conventional algorithm. Additionally, in indoor environments, the proposed algorithm provides a detailed representation of the indoor multipath, outperforming conventional algorithms. The high-resolution radar imaging offered by the proposed method will enable improved target recognition and thus enhance overall performance in practical applications.