In this article, a terahertz transmit-array antenna (TAA) with a specific beamwidth and good beamwidth uniformity is developed for the feed source of a Cassegrain antenna. The TAA consists of a transmit surface fed by an open-ended waveguide (OEWG). The polarization-conversion elements are constructed with L-shaped and grated patterns on the two sides of a polyimide (PI) film, to provide the full phase coverage of 360° and the transmission magnitudes of −5.5 to −2.6 dB. The PI film prototype with conductive patterns is fabricated in house, and a high process precision of $5~\mu \text{m}$ is achieved. The relative permittivity and loss tangent of the PI film are measured to be $\varepsilon _{\text {r}}$ = 3.323 and $\tan \delta $ = 0.035 around 300 GHz using the free space method before design. The scale of the transmit surface is determined according to the relationship between the beamwidth and aperture size of antennas. The radiation patterns of the developed TAA in the planes of $\varphi $ = 0° and $\varphi $ = 90° are measured, with good agreement obtained between the measured and simulated results. The TAA achieves the desired beamwidth and the beamwidth uniformity of 15° and ±10%, respectively, within the frequency band of 305–317 GHz, and the maximum measured gain is 19.15 dBi at 312 GHz.