This article presents a deep neural network‐based constant false alarm rate (NNB‐CFAR) detector for simulated high‐frequency surface wave radar (HFSWR) data. A deep neural network is trained to identify fluctuation parameters of each cell of a range‐Doppler power spectrum based on the patterns present in the neighbouring cells. The estimated parameters are then used for calculating a detection threshold with a user‐specified probability of false alarm. To train the network, a realistic model of HFSWR echoes is used for generating a large labelled range‐Doppler image dataset, including many possible clutter scenarios and interfering target echoes. Several CFAR windows are extracted from the training range‐Doppler dataset and used as training data. The neural network is trained to replicate the output of a maximum likelihood estimator based on the reference cells of the CFAR window. The NNB‐CFAR algorithm was then compared to traditional CFAR algorithms by identifying targets in the second set of simulated range‐Doppler images. The probability of detection was also experimentally measured in the context of HFSWR for all algorithms. Results show that the technique can significantly improve detection rates amid strong clutter.