Structural health monitoring (SHM) and vibration-based structural damage detection have been a continuous interest for civil, mechanical and aerospace engineers over the decades. Early and meticulous damage detection has always been one of the principal objectives of SHM applications. The performance of a classical damage detection system predominantly depends on the choice of the features and the classifier. While the fixed and hand-crafted features may either be a sub-optimal choice for a particular structure or fail to achieve the same level of performance on another structure, they usually require a large computation power which may hinder their usage for real-time structural damage detection. This paper presents a novel, fast and accurate structural damage detection system using 1D Convolutional Neural Networks (CNNs) that has an inherent adaptive design to fuse both feature extraction and classification blocks into a single and compact learning body. The proposed method performs vibration-based damage detection and localization of the damage in real-time. The advantage of this approach is its ability to extract optimal damage-sensitive features automatically from the raw acceleration signals. Large-scale experiments conducted on a grandstand simulator revealed an outstanding performance and verified the computational efficiency of the proposed real-time damage detection method.