The potential of ultrasound tomography has been noticed to quantify the tissue acoustic properties for advanced clinical diagnosis. However, the location of most of the human anatomies limits the tomography for a few angles that leads the reconstruction as a more challenging problem. In this work, a deep convolutional neural networks- based technique is presented to estimate the speed of sound of tissue from a limited angle projection data. The underlying concept is based on filtered back projection technique, where the convolutional neural network is used to model the high-pass filter before the back projection. Moreover, we use a post convolutional neural network to suppress the artifacts generated due to the limited angle tomography. We train the network from a set of simulation experiments; on the test set consisting of 1,750 simulation experiments, we achieve an average mean absolute error of 2.1% in predicting the speed of sound map.