Double-line spectroscopic binaries (SB2s) are a vital class of spectroscopic binaries for studying star formation and evolution. Searching for SB2s has been a hot topic in astronomy. Although considerable efforts have been made with fruitful outcomes, limitations in automation and accuracy still persist. In this study, we developed a convolutional neural network model to search for SB2 candidates in LAMOST medium-resolution survey (MRS) data release (DR) 9 v1.0 by detecting double peaks in the cross-correlation function (CCF). We first generated a large number of spectra of single stars and binaries using the iSpec spectral synthesis software. The CCFs of these synthesized spectra were then calculated to form our training set. To efficiently detect the peaks of the CCFs, we applied a Softmax function-based noise reduction method. After testing and validation, the model achieved an accuracy of 97.76% in the testing set and was validated for more than 90% of the sample in several published SB2 catalogs. Finally, by applying the model to examine approximately 1.59 million LAMOST-MRS DR9 spectra, we identified 728 candidate SB2s, including 281 newly discovered ones.