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We present a bent ray reconstruction algorithm for an ultrasound tomography (UT) scanner designed for breast screening. The scanner consists of a circular array of transmitters and receivers which encloses the object to be imaged. By solving a nonlinear system of equations, the reconstruction algorithm estimates the sound speed of the object using the set of travel-time measurements. The main difficulty in this inverse problem is to ensure the convergence and robustness to noise. In this paper, we propose a gradient method to find a solution for which the corresponding travel-times are closest to the measured travel-times in the least squares sense. To this end, first the gradient of the cost function is derived using Fermat's Principle. Then, the iterative nonlinear conjugate gradient algorithm solves the minimization problem. This is combined with the backtracking line search method to efficiently find the step size in each iteration. This approach is guaranteed to converge to a local minimum of the cost function where the convergence point depends on the initial guess. Moreover, the method has the potential to easily incorporate regularity constraints such as sparsity as a priori information on the model. The method is tested both numerically and using in vivo data obtained from a UT scanner. The results confirm the stability and robustness of our approach for breast screening applications.