This paper presents a novel periodic grounded coplanar waveguide (GCPW) leaky-wave antenna implemented in an Indium Phosphide (InP) process. The antenna is designed to operate in the 220 GHz–325 GHz frequency range, with the goal of integrating it with an InP uni-traveling-carrier photodiode to realize a wireless transmitter module. Future wireless communication systems must deliver a high data rate to multiple users in different locations. Therefore, wireless transmitters need to have a broadband nature, high gain, and beam-steering capability. Leaky-wave antennas offer a simple and cost-effective way to achieve beam-steering by sweeping frequency in the THz range. In this paper, the first periodic GCPW leaky-wave antenna in the 220 GHz–325 GHz frequency range is demonstrated. The antenna design is based on a novel GCPW leaky-wave unit cell (UC) that incorporates mirrored L-slots in the lateral ground planes. These mirrored L-slots effectively mitigate the open stopband phenomenon of a periodic leaky-wave antenna. The leakage rate, phase constant, and Bloch impedance of the novel GCPW leaky-wave UC are analyzed using Floquet’s theory. After optimizing the UC, a periodic GCPW leaky-wave antenna is constructed by cascading 16 UCs. Electromagnetic simulation results of the leaky-wave antenna are compared with an ideal model derived from a single UC. The two design approaches show excellent agreement in terms of their reflection coefficient and beam-steering range. Therefore, the ideal model presented in this paper demonstrates, for the first time, a rapid method for developing periodic leaky-wave antennas. To validate the simulation results, probe-based antenna measurements are conducted, showing close agreement in terms of the reflection coefficient, peak antenna gain, beam-steering angle, and far-field radiation patterns. The periodic GCPW leaky-wave antenna presented in this paper exhibits a high gain of up to 13.5 dBi and a wide beam-steering range from −60° to 35° over the 220 GHz–325 GHz frequency range.