Glottal Closure Instants (GCIs) correspond to the temporal locations of significant excitation to the vocal tract occurring during the production of voiced speech. GCI detection from speech signals is a well-studied problem given its importance in speech processing. Most of the existing approaches for GCI detection adopt a two-stage approach (i) Transformation of speech signal into a representative signal where GCIs are localized better, (ii) extraction of GCIs using the representative signal obtained in first stage. The former stage is accomplished using signal processing techniques based on the principles of speech production and the latter with heuristic-algorithms such as dynamic-programming and peak-picking. These methods are thus task-specific and rely on the methods used for representative signal extraction. However, in this paper, we formulate the GCI detection problem from a representation learning perspective where appropriate representation is implicitly learned from the raw-speech data samples. Specifically, GCI detection is cast as a supervised multi-task learning problem solved using a deep convolutional neural network jointly optimizing a classification and regression cost. The learning capability is demonstrated with several experiments on standard datasets. The results compare well with the state-of-the-art algorithms while performing better in the case of presence of real-world non-stationary noise.