This paper proposes a novel SAPNet model that incorporates a stochastic area pooling (SAP) method with a generic stacked T-shaped CNN architecture. In our SAP method, pooling area is randomly transformed and max pooling operation is then conducted on such areas, which are no longer regular identical fixed upright squares. It can be viewed as feature-level augmentation, substantially reducing model parameters while keeping generalization ability of CNN almost unchanged. Furthermore, we present a generic CNN architecture that structurally resembles three stacked T-shaped cubes. In such architecture, the number of kernels in convolutional layer preceding any pooling layer is doubled and all learnable weight layers are combined with batch normalization and dropout with a small ratio. Finally, on CIFAR-10, CIFAR-100, MNIST, and SVHN datasets, the experimental results show that our SAPNet requires fewer parameters than regular CNN models and still achieves superior recognition performances for all the four benchmarks.