Warm current has a strong impact on the melting of sea ice, so clarifying the current features plays a very important role in the Arctic sea ice coverage forecasting study field. Currently, Arctic acoustic tomography is the only feasible method for the large-range current measurement under the Arctic sea ice. Furthermore, affected by the high latitudes Coriolis force, small-scale variability greatly affects the accuracy of Arctic acoustic tomography. However, small-scale variability could not be measured by empirical parameters and resolved by Regularized Least Squares (RLS) in the inverse problem of Arctic acoustic tomography. In this paper, the convolutional neural network (CNN) is proposed to enhance the prediction accuracy in the Arctic, and especially, Gaussian noise is added to reflect the disturbance of the Arctic environment. First, we use the finite element method to build the background ocean model. Then, the deep learning CNN method constructs the non-linear mapping relationship between the acoustic data and the corresponding flow velocity. Finally, the simulation result shows that the deep learning convolutional neural network method being applied to Arctic acoustic tomography could achieve 45.87% accurate improvement than the common RLS method in the current inversion.