Chronic insomnia can significantly impair an individual's quality of life leading to a high societal cost. Unfortunately, limited automated tools exist that can assist clinicians in the timely detection of insomnia. In this paper, we propose a two stage approach to automatically detect insomnia from an overnight EEG recording. In the first stage we trained a sleep stage scoring model and an epoch-level insomnia detection model. Both models are deep neural network (DNN)- based which are fed by a set of temporal and spectral features derived from 2 EEG channels. In the second stage we computed two subject-level feature sets. One is computed using the output of the sleep stage scoring model and consists of the sleep stage ratios, the stage pair ratios and the stage transition ratios. The second feature set is derived from the output of the epoch-level insomnia detection model and represents the ratio of detected insomniac epochs in each stage and their average posterior probability. These features are then used to train a final binary classifier to classify each subject as control, i.e., with no sleep complaints, or insomniac. We compared 5 different binary classifiers, namely the linear discriminant analysis (LDA), the classification and regression trees (CART) and the support vector machine (SVM) with linear, Gaussian and sigmoid kernels. The system was evaluated against data collected from 115 participants, 61 control and 54 with insomnia, and achieved $F1$ score, sensitivity and specificity of 0.88, 84% and 91% respectively.