An approach based on limited-angle transmission tomography for reconstruction of the sound velocity distribution in the breast is proposed. The imaging setup allows acoustic data acquisition for simultaneous B-mode image formation and the tomographic sound velocity reconstruction. The time-of-flight data are acquired by a linear array positioned at the top of the compressed breast that both transmits and receives, and a metal plate is placed at the bottom as a reflector. In order to improve the sound velocity estimation accuracy, a reconstruction algorithm based on a convex programming formulation has been developed. Simulations for both imaging and time-of-flight data based on a 5-MHz linear array were performed. Effects of wave propagation such as refraction and diffraction were included in the generated data. Results show that the proposed approach is both feasible and accurate. The approach can be used to complement conventional B-mode imaging to enhance the detection of breast cancer.