Remote sensing of heartbeat offers various applications in the medical and health care fields. To realize non-contact heartbeat detection, an FMCW (Frequency Modulated Continuous Wave) radar-based heartbeat detection method has been investigated. The conventional FMCW radar-based heartbeat detection method estimates a range from an FMCW radar to a subject and extracts heartbeat components from phase changes for the range. However, the range suitable for extracting heartbeat components can change over time due to respiration and body fluctuation. Thus, when the SNR (Signal-to-Noise Ratio) of heartbeat components over phase changes is low at the estimated range, the accuracy of heartbeat detection tends to degrade. In this paper, we propose a MIMO (Multiple-Input Multiple-Output) FMCW radar-based heartbeat detection method based on space diversity. A MIMO FMCW radar can estimate the range for multiple beam directions and obtain phase changes for a space specified with the range and the beam direction. The SNR of heartbeat components over phase changes differs from one space to another. Taking it into account, the proposed method detects heartbeat by exploiting the space diversity of phase changes. The experimental results showed that compared to the detection method using only one phase change, the proposed method using phase changes for multiple spaces detected heartbeat accurately, which is brought by the diversity effect of phase changes for multiple spaces.