Among the most common cancers, colorectal cancer (CRC) has a high death rate. The best way to screen for colorectal cancer (CRC) is with a colonoscopy, which has been shown to lower the risk of the disease. As a result, Computer-aided polyp classification technique is applied to identify colorectal cancer. But visually categorizing polyps is difficult since different polyps have different lighting conditions. Different from previous works, this article presents Enhanced Scattering Wavelet Convolutional Neural Network (ESWCNN), a polyp classification technique that combines Convolutional Neural Network (CNN) and Scattering Wavelet Transform (SWT) to improve polyp classification performance. This method concatenates simultaneously learnable image filters and wavelet filters on each input channel. The scattering wavelet filters can extract common spectral features with various scales and orientations, while the learnable filters can capture image spatial features that wavelet filters may miss. A network architecture for ESWCNN is designed based on these principles and trained and tested using colonoscopy datasets (two public datasets and one private dataset). An n-fold cross-validation experiment was conducted for three classes (adenoma, hyperplastic, serrated) achieving a classification accuracy of 96.4%, and 94.8% accuracy in two-class polyp classification (positive and negative). In the three-class classification, correct classification rates of 96.2% for adenomas, 98.71% for hyperplastic polyps, and 97.9% for serrated polyps were achieved. The proposed method in the two-class experiment reached an average sensitivity of 96.7% with 93.1% specificity. Furthermore, we compare the performance of our model with the state-of-the-art general classification models and commonly used CNNs. Six end-to-end models based on CNNs were trained using 2 dataset of video sequences. The experimental results demonstrate that the proposed ESWCNN method can effectively classify polyps with higher accuracy and efficacy compared to the state-of-the-art CNN models. These findings can provide guidance for future research in polyp classification.