Rapid classification of tumors that are detected in the medical images is of great importance in the early diagnosis of the disease. In this paper, a new liver and brain tumor classification method is proposed by using the power of convolutional neural network (CNN) in feature extraction, the power of discrete wavelet transform (DWT) in signal processing, and the power of long short-term memory (LSTM) in signal classification. A CNN-DWT-LSTM method is proposed to classify the computed tomography (CT) images of livers with tumors and to classify the magnetic resonance (MR) images of brains with tumors. The proposed method classifies liver tumors images as benign or malignant and then classifies brain tumor images as meningioma, glioma, and pituitary. In the hybrid CNN-DWT-LSTM method, the feature vector of the images is obtained from pre-trained AlexNet CNN architecture. The feature vector is reduced but strengthened by applying the single-level one-dimensional discrete wavelet transform (1-D DWT), and it is classified by training with an LSTM network. Under the scope of the study, images of 56 benign and 56 malignant liver tumors that were obtained from Fırat University Research Hospital were used and a publicly available brain tumor dataset were used. The experimental results show that the proposed method had higher performance than classifiers, such as K-nearest neighbors (KNN) and support vector machine (SVM). By using the CNN-DWT-LSTM hybrid method, an accuracy rate of 99.1% was achieved in the liver tumor classification and accuracy rate of 98.6% was achieved in the brain tumor classification. We used two different datasets to demonstrate the performance of the proposed method. Performance measurements show that the proposed method has a satisfactory accuracy rate at the liver tumor and brain tumor classifying.