<p>Camera translation averaging aims at recovering the global camera locations from an input set of noisy relative camera translation directions. Existing works in literature generally estimate the global camera locations via time-consuming nonlinear optimizations on geometrical-constraint-based cost functions. However, their computational costs increase significantly with the increase of the input relative translation directions. To address this problem, we attempt to bridge the gap between deep learning and camera translation averaging in this paper, inspired by the fast inference speed and superior performance of deep neural networks in other visual tasks. Firstly, we reveal a basic property of the translation averaging problem, called Reverse-Direction-Invariance (RDI). Then, based on this RDI property, a deep network for translation averaging is proposed, called DeepTA, which consists of multiple location optimization blocks and an RDI-embedding block. The location optimization blocks are designed to predict the global camera locations gradually, while the RDI-embedding block is designed to impose the RDI property on each location optimization block for boosting its performance. Moreover, we theoretically prove that DeepTA is reverse-direction-invariant. Extensive experimental results demonstrate that the proposed DeepTA does not only achieve a higher accuracy than several state-of-the-art methods, but also a <b>100</b><InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{\times }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo mathvariant="bold">×</mo> </mrow> </math></EquationSource> </InlineEquation> (or even more) acceleration in most cases.</p>