Sign language is the main communication method for deaf people. It is a collection of signs that deaf people use to deal with each other. Deaf people find it difficult to communicate with normal people, as most of them do not understand the signs of the sign language. Sign language recognition systems translate the signs into natural languages and thus shorten the gap between deaf and normal people. Many studies have been done on different sign languages. There is a considerable number of studies on the standard Arabic sign language. In Saudi Arabia, deaf people use the Saudi language, which is different from standard Arabic. This study proposes a smart recognition system for Saudi sign language based on convolutional neural networks. The system is based on the Saudi Sign language dictionary, which was published recently in 2018. In this study, we constructed a dataset of 40 Saudi signs with about 700 images for each sign. We then developed a deep convolutional neural network and trained it on the constructed dataset. To have better recognition, we took images of the signs with different hand sizes, skin colors, lighting, backgrounds, and with/without accessories. The results showed that the recognition model achieved an accuracy of 97.69% for training data and 99.47% for testing data. The model was implemented in two versions: mobile and desktop.