The application of radar in the medical field has attracted a lot of attention recently. Vital sign detection and monitoring are essential for certain use cases. Due to the limitations and discomfort during contact-based vital sign monitoring, the non-contact approach becomes preferred. In this work, a signal processing approach for multi-target breathing rate and heart rate monitoring is proposed. The proposed approach uses a frequency modulated continuous wave (FMCW) radar for contact-less vital sign monitoring. Using the proposed approach, the vital signs of multiple persons can be monitored simultaneously using a single mmWave radar. The results obtained using the proposed approach show an excellent match compared to a medical-grade instrument. This is especially notable for the heart rate monitoring, where the achieved accuracy error is only 7.77 %, outperforming other similar works.