A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly available. Performance evaluation for several widely known datasets is provided, showing several relevant features: i) for small / medium input image sizes the proposed network gives very good testing accuracy, given a low implementation complexity and model size; ii) compares favorably with other widely known resources-constrained models, for instance in comparison to MobileNetv2 provides better accuracy with several times less training times and up to ten times less parameters (memory occupied by the model); iii) has a relevant set of hyper-parameters which can be easily and rapidly tuned due to the fast training specific to it. All these features make NL-CNN suitable for IoT, smart sensing, bio-medical portable instrumentation and other applications where artificial intelligence must be deployed in energy-constrained environments.