Ultrasound computed tomography (UCT) has attracted increasing attention due to its potential for early breast cancer diagnosis and screening. Synthetic aperture imaging is a widely used means for reflection UCT image reconstruction, due to its ability to produce isotropic and high-resolution anatomical images. However, obtaining fully sampled UCT data from all directions over multiple transmissions is a time-consuming scanning process. Even though sparse transmission strategy could mitigate the data acquisition complication, image quality reconstructed by traditional Delay and Sum (DAS) methods may degrade substantially. This study presents a deep learning framework based on a conditional generative adversarial network, UCT-GAN, to efficiently reconstruct reflection UCT image from sparse transmission data. The evaluation experiments using breast imaging data in vivo show that the proposed UCT-GAN is able to generate high-quality reflection UCT images when using 8 transmissions only, which are comparable to that reconstructed from the data acquired by 512 transmissions. Quantitative assessment in terms of peak signal-to-noise ratio (PSNR), normalized mean square error (NMSE), and structural similarity index measurement (SSIM) show that the proposed UCT-GAN is able to efficiently reconstruct high-quality reflection UCT images from sparsely available transmission data, outperforming several other methods, such as RED-GAN, DnCNN-GAN, BM3D. In the experiment of 8-transmission sparse data, the PSNR is 29.52 dB, and the SSIM is 0.7619. The proposed method has the potential of being integrated into the UCT imaging system for clinical usage.