We introduce DeepSPEC, a novel convolutional neural network (CNN) -based approach for frequency-and-phase correction (FPC) of MRS spectra to achieve fast and accurate FPC of single-voxel PRESS MRS and MEGA-PRESS data. In DeepSPEC, two neural networks, including one for frequency correction and one for phase correction were trained and validated using published simulated and in vivo PRESS and MEGA-PRESS MRS dataset with wide-range artificial frequency and phase offsets applied. DeepSPEC was subsequently tested and compared to the current deep learning solution - a ″vanilla″ neural network approach using multilayer perceptrons (MLP). Furthermore, random noise was added to the original simulated dataset to further investigate the model performance with noise at varied signal-to-noise (SNR) levels (i.e., 6 dB, 3 dB, and 1.5 dB). The testing showed that DeepSPEC is more robust to noise compared to the MLP-based approach due to having a smaller absolute error in both frequency and phase offset prediction. The DeepSPEC framework was capable of correcting frequency offset with 0.01±0.01 Hz and phase offset with 0.12±0.09° absolute errors on average for unseen simulated data at a high SNR (12 dB) and correcting frequency offset with 0.01±0.02 Hz and phase offset within -0.07±0.44° absolute errors on average at very low SNR (1.5 dB). Furthermore, additional frequency and phase offsets (i.e., small, moderate, large) were applied to the in vivo dataset, and DeepSPEC demonstrated better performance for FPC when compared to the MLP-based approach. Results also show DeepSPEC has superior performance than the model-based SR implementation (mSR) in FPC by having higher accuracy in a wider range of additional offsets. These results represent a proof of concept for the use of CNNs for preprocessing MRS data and demonstrate that DeepSPEC accurately predicts frequency and phase offsets at varying noise levels with state-of-the-art performance.