In this paper, Artificial Neural Networks are used to solve DELAY Differential Equations. We have suggested an appropriate approximation function based on ANN and then by solving an optimization problem of error function, the neural network is trained. The advantage of this technique is that the proposed approximation functions, with a slight modification, can be used for most types of DELAY differential equations, including DDE with constant DELAY, time-dependent DELAY and pantograph DELAY. To demonstrate the effectiveness of the method, various examples have been tested and the validity and efficiency of the method have been shown.