Respiration and heartbeats rates are important physiological assessment indicators that provide valid prior-knowledge for the diagnosis of numerous diseases. However, most of the current research focuses on the vital signs measurement of single target, and multi-target vital signs detection has not received much attention. In this paper, we use frequency-modulated continuous wave (FMCW) radar to measure the vital signs signals of multi-target. First, we apply the three-dimensional fast Fourier transform (3D-FFT) method to separate multiple targets and get their distance and azimuth information. Subsequently, the linear constrained minimum variance-based adaptive beamforming (LCMV-ADBF) technique is proposed to form a spatially distributed beams on the targets of interest directions. Finally, a compressive sensing based on orthogonal matching pursuit (CS-OMP) method and rigrsure adaptive soft threshold noise reduction based on discrete wavelet transform (RA-DWT) method are present to extract the respiratory and heartbeat signals. We perform tests in a real experimental environment and compare the proposed method with reference devices. The results show that the degrees of agreement for respiratory and heartbeat are 89% and 87%, respectively, for two human targets. The level of agreement for respiratory and heartbeat is 87% and 85%, respectively, for three human targets, proving the effectiveness of the proposed method.