Direction of arrival (DOA) estimation of wireless signals has a long history but is still being investigated to improve the estimation accuracy. Non-linear algorithms such as compressed sensing are now applied to DOA estimation and achieve very high performance. If the large computational loads of compressed sensing algorithms are acceptable, it may be possible to apply a deep neural network (DNN) to DOA estimation. In this paper, we verify on-grid DOA estimation capability of the DNN under a simple estimation situation and discuss the effect of training data on DNN design. Simulations show that SNR of the training data strongly affects the performance and that the random SNR data is suitable for configuring the general-purpose DNN. The obtained DNN provides reasonably high performance, and it is shown that the DNN trained using the training data restricted to close DOA situations provides very high performance for the close DOA cases.