Cancer tumor classification based on morphological characteristics alone has been shown to have serious limitations. Breast, lung, colorectal, thyroid, and ovarian are the most commonly diagnosed cancers among women. Precise classification of cancers into their types is considered a vital problem for cancer diagnosis and therapy. In this paper, we proposed a stacking ensemble deep learning model based on one-dimensional convolutional neural network (1D-CNN) to perform a multi-class classification on the five common cancers among women based on RNASeq data. The RNASeq gene expression data was downloaded from Pan-Cancer Atlas using GDCquery function of the TCGAbiolinks package in the R software. We used least absolute shrinkage and selection operator (LASSO) as feature selection method. We compared the results of the new proposed model with and without LASSO with the results of the single 1D-CNN and machine learning methods which include support vector machines with radial basis function, linear, and polynomial kernels; artificial neural networks; k-nearest neighbors; bagging trees. The results show that the proposed model with and without LASSO has a better performance compared to other classifiers. Also, the results show that the machine learning methods (SVM-R, SVM-L, SVM-P, ANN, KNN, and bagging trees) with under-sampling have better performance than with over-sampling techniques. This is supported by the statistical significance test of accuracy where the p-values for differences between the SVM-R and SVM-P, SVM-R and ANN, SVM-R and KNN are found to be p = 0.003, p =  < 0.001, and p =  < 0.001, respectively. Also, SVM-L had a significant difference compared to ANN p = 0.009. Moreover, SVM-P and ANN, SVM-P and KNN are found to be significantly different with p-values p =  < 0.001 and p =  < 0.001, respectively. In addition, ANN and bagging trees, ANN and KNN were found to be significantly different with p-values p =  < 0.001 and p = 0.004, respectively. Thus, the proposed model can help in the early detection and diagnosis of cancer in women, and hence aid in designing early treatment strategies to improve survival.