In this paper, we propose a classification based glottal closure instants (GCI) detection from pathological acoustic speech signal, which finds many applications in vocal disorder analysis. Till date, GCI for pathological disorder is extracted from laryngeal (glottal source) signal recorded from Electroglottograph, a dedicated device designed to measure the vocal folds vibration around the larynx. We have created a pathological dataset which consists of simultaneous recordings of glottal source and acoustic speech signal of six different disorders from vocal disordered patients. The GCI locations are manually annotated for disorder analysis and supervised learning. We have proposed convolutional neural network based GCI detection method by fusing deep acoustic speech and linear prediction residual features for robust GCI detection. The experimental results showed that the proposed method is significantly better than the state-of-the-art GCI detection methods.