Noncontact monitoring of human vital signs has been an emerging research topic in recent years. A key approach to this monitoring is the use of the Doppler radar concept which enables real-time vital signs detection, resulting in a new class of radar system known as bio-radar. The antennas are a key component of any bio-radar module and their designs should meet the common requirements of bio-radar applications such as high radiation directivity and mechanical flexibility. This paper presents the design of a four-element antenna array on a flexible liquid crystal polymer (LCP) substrate of 100 μm thickness and εr of 3.35. The designed antenna array can be used with a 24 GHz bio-radar for vital signs monitoring in a non-contact manner. It features a relatively compact size of 36.5 × 53 mm2 and measured gain of 5.81 dBi. The two vital signs: breathing rate (BR) and heart rate (HR) of two human subjects are detected with relatively good accuracy using the fabricated antenna array and radio frequency (RF) output power of −3 dBm from a distance of approximately 60 cm. The effect of bending on the antenna performance is also analyzed.