Delamination is one of the detrimental defects in laminated composite materials that often arose due to manufacturing defects or in-service loadings (e.g., low/high velocity impacts). Most of the contemporary research efforts are dedicated to high-frequency guided wave and mode shape-based methods for the assessment (i.e., detection, quantification, localization) of delamination. This paper presents a deep learning framework for structural vibration-based assessment of delamination in smart composite laminates. A number of small-sized (4.5% of total area) inner and edge delaminations are simulated using an electromechanically coupled model of the piezo-bonded laminated composite. Healthy and delaminated structures are stimulated with random loads and the corresponding transient responses are transformed into spectrograms using optimal values of window size, overlapping rate, window type, and fast Fourier transform (FFT) resolution. A convolutional neural network (CNN) is designed to automatically extract discriminative features from the vibration-based spectrograms and use those to distinguish the intact and delaminated cases of the smart composite laminate. The proposed architecture of the convolutional neural network showed a training accuracy of 99.9%, validation accuracy of 97.1%, and test accuracy of 94.5% on an unseen data set. The testing confusion chart of the pre-trained convolutional neural network revealed interesting results regarding the severity and detectability for the in-plane and through the thickness scenarios of delamination.