A two-dimensional (2D) optical true-time delay (TTD) beam-forming system using a compact fiber grating prism (FGP) for a planar phased array antenna (PAA) is proposed. The optical beam-forming system mainly consists of a TTD unit based on the same compact FGP, one tunable laser for elevation beam steering, and a controlled wavelength converter for azimuth beam steering. A planar PAA using such 2D optical TTD unit has advantages such as compactness, low bandwidth requirement for tunable laser sources, and potential for large-scale system implementations. The proof-of-concept experiment results demonstrate the feasibility of the proposed scheme.