Gradient-based traveltime tomography, which aims to minimize the difference between modeled and observed first-arrival times, is a highly nonlinear optimization problem. Stabilization of this inverse problem often requires using regularization. Although regularization helps avoid local minima solutions, it might cause low-resolution tomograms because of its inherent smoothing property. However, although conventional ray-based tomography can be robust in terms of the uniqueness of the solution, it suffers from the limitations inherent in ray tracing, which limits its use in complex media. To mitigate the aforementioned drawbacks of gradient and ray-based tomography, we have approached the problem in a novel way leveraging data-driven inversion techniques based on training deep convolutional neural networks (DCNN). Because DCNN often face challenges in detecting high-level features from the relatively smooth traveltime data, we use this type of network to map horizontal changes in observed first-arrival traveltimes caused by a source shift to lateral velocity variations. The relationship between them is explained by a linearized eikonal equation. Construction of the velocity models from this predicted lateral variation requires information from, for example, a vertical well log in the area. This vertical profile is then used to build a tomogram from the output of the network. The synthetic and field data results verify that the suggested approach reliably estimates the velocity models. Because of the limited depth penetration of first-arrival traveltimes, the method is particularly favorable for near-surface applications.