Respiration-induced B fluctuation corrupts MRI images by inducing phase errors in k-space. A few approaches such as navigator have been proposed to correct for the artifacts at the expense of sequence modification. In this study, a new deep learning method, which is referred to as DeepResp, is proposed for reducing the respiration-artifacts in multi-slice gradient echo (GRE) images. DeepResp is designed to extract the respiration-induced phase errors from a complex image using deep neural networks. Then, the network-generated phase errors are applied to the k-space data, creating an artifact-corrected image. For network training, the computer-simulated images were generated using artifact-free images and respiration data. When evaluated, both simulated images and in-vivo images of two different breathing conditions (deep breathing and natural breathing) show improvements (simulation: normalized root-mean-square error (NRMSE) from 7.8 ± 5.2% to 1.3 ± 0.6%; structural similarity (SSIM) from 0.88 ± 0.08 to 0.99 ± 0.01; ghost-to-signal-ratio (GSR) from 7.9 ± 7.2% to 0.6 ± 0.6%; deep breathing: NRMSE from 13.9 ± 4.6% to 5.8 ± 1.4%; SSIM from 0.86 ± 0.03 to 0.95 ± 0.01; GSR 20.2 ± 10.2% to 5.7 ± 2.3%; natural breathing: NRMSE from 5.2 ± 3.3% to 4.0 ± 2.5%; SSIM from 0.94 ± 0.04 to 0.97 ± 0.02; GSR 5.7 ± 5.0% to 2.8 ± 1.1%). Our approach does not require any modification of the sequence or additional hardware, and may therefore find useful applications. Furthermore, the deep neural networks extract respiration-induced phase errors, which is more interpretable and reliable than results of end-to-end trained networks.