Breast cancer is a significant cause of death among women worldwide. It is crucial to quickly and accurately diagnose breast cancer in order to reduce mortality rates. While traditional diagnostic techniques for medical imaging and pathology samples have been commonly used in breast cancer screening, they still have certain limitations. Surface-enhanced Raman spectroscopy (SERS) is a fast, highly sensitive and user-friendly method that is often combined with deep learning techniques like convolutional neural networks. This combination helps identify unique molecular spectral features, also known as "fingerprint", in biological samples such as serum. Ultimately, this approach is able to accurately screen for cancer. The Gramian angular field (GAF) algorithm can convert one-dimensional (1D) time series into two-dimensional (2D) images. These images can be used for data visualization, pattern recognition and machine learning tasks. In this study, 640 serum SERS from breast cancer patients and healthy volunteers were converted into 2D spectral images by Gramian angular field (GAF) technique. These images were then used to train and test a two-dimensional convolutional neural network-GAF (2D-CNN-GAF) model for breast cancer classification. We compared the performance of the 2D-CNN-GAF model with other methods, including one-dimensional convolutional neural network (1D-CNN), support vector machine (SVM), K-nearest neighbor (KNN) and principal component analysis-linear discriminant analysis (PCA-LDA), using various evaluation metrics such as accuracy, precision, sensitivity, F1-score, receiver operating characteristic (ROC) curve and area under curve (AUC) value. The results showed that the 2D-CNN model outperformed the traditional models, achieving an AUC value of 0.9884, an accuracy of 98.13%, sensitivity of 98.65% and specificity of 97.67% for breast cancer classification. In this study, we used conventional nano-silver sol as the SERS-enhanced substrate and a portable laser Raman spectrometer to obtain the serum SERS data. The 2D-CNN-GAF model demonstrated accurate and automatic classification of breast cancer patients and healthy volunteers. The method does not require augmentation and preprocessing of spectral data, simplifying the processing steps of spectral data. This method has great potential for accurate breast cancer screening and also provides a useful reference in more types of cancer classification and automatic screening.