This study is motivated by the need to develop a data-driven deep-learning approach for vibration-based structural health monitoring of a steel frame structure with bolted connections. A convolutional-neural-network-based deep-learning architecture is designed and trained to extract discriminative features from the vibration-based time-frequency scalogram images and use those to distinguish the undamaged and damaged cases of the targeted frame structure. Different damage and undamaged classes corresponding to the loosening of bolts are categorized as fully loose, hand tight, and fully tight (undamaged) conditions. The average training and validation accuracy were found to be 100% and 98.1%, respectively. In order to check the performance and robustness of the technique, testing is carried out for an unseen dataset corresponding to the training classes as well as some additional cases close to the training classes. The proposed deep-learning approach can successfully classify the damage classes with high testing accuracy that demonstrates its efficacy as an automation tool for health monitoring of connections of plane frame structures.