In recent years, radar, especially frequency-modulated continuous wave (FMCW) radar, has been extensively used in non-contact vital signs (NCVS) research. However, current research does not work when multiple human targets are close to each other, especially when adjacent human targets lie in the same resolution cell. In this paper, a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)–independent component analysis (ICA) was proposed to obtain the vital-sign information (including respiratory rate and heart rate) of adjacent human targets by using a single FMCW radar. Firstly, the data observed at a single angle were decomposed by the CEEMDAN separation algorithm to construct virtual multi-angle observations. It can effectively transform the undetermined blind source separation (UBSS) problem into an overdetermined blind source separation (BSS) problem. Thus, a BSS algorithm based on FastICA can be used to reconstruct each person’s vital-sign signal and then calculate their respiratory rate/heart rate. To validate the effectiveness of the proposed method, experiments based on the measured data were conducted and the results show that the proposed method can obtain multi-target vital-sign information even when they are in the same resolution cell.