Conversion devices between free-space microwave/ millimeter-wave and lightwave signals are required in Fiber-Wireless (Fi-Wi) links. In this paper, we propose a free-space millimeter-wave Electro-Optic (EO) modulator using Quasi-Phase-Matching (QPM) gap-embedded-patch-antennas on a low dielectric constant substrate. Free-space millimeter-wave signals can be received and converted directly to lightwave signals using the proposed device. It can be operated passively with no external power supply and operated with extremely low millimeter-wave losses. The QPM array structure can be adopted for improving modulation efficiency by considering the transit-time effects. The proposed device is easy connected to optical fiber, therefore Fi-Wi can be realized using the proposed device. Basic structure, analysis, and experimental results of the proposed device are discussed and reported for 40 GHz operational millimeter-wave bands.