Differences between indoor non-contact vital sign sensor and general sensors are ¡§indoor¡¨ and ¡§vital sign¡¨. In indoor environment, receiving signals encounter multipath problem caused by the reflection of walls and furniture. Two main vital signs that we are concerned with are heartbeat and respiration; both of them are weaker than general signals used in communication. To overcome problems caused by multipath and weak signal strength, in this thesis, we design a narrow beamwidth antenna operating at 2.45 GHz for indoor non-contact vital sign sensor. We propose a ground surrounded antenna (GSA) which differs from traditional slot and patch antenna. The proposed GSA excites slot mode and patch mode at the same time, so that we can achieve dual-bands or wide band by adjusting its physical parameters. Meanwhile, the reflected wave bounced back from the surrounding ground plane can cause constructive interference so that the antenna possesses better gain and beamwidth. Using GSA as the unit antenna of antenna array to achieve narrow beamwidth design, and adding the concept of superstrate can enhance antenna gain and reduce backlobe radiation. The minimum beamwidth at two orthogonal planes are 26 and 52 degrees respectively, and the antenna gain achieves 12.2 dBi. To reduce the interference between receiving and transmitting signals in single antenna, we use two separate antennas. Finally, we discuss and improve isolation problem between two antennas.