A non-linear damage detection method for cracks of the concrete simply-supported bridge based on the improved Hilbert-Huang transfer (HHT) is proposed in this work. The curvilinear breathing crack model controlled by curvature is employed to consider the breathing phenomenon of cracks, and the model is integrated into vehicle-bridge interaction system to simulate operational environment. The mirror extension and ensemble empirical mode decomposition algorithm are introduced to eliminate the end effect and mode mixing problems respectively. The energy time history from the acceleration response of the bridge under operational condition is acquired using the improved HHT algorithm, and then the appearance time and relative amplitude ratio from the peak of the energy time history are extracted as features to localize and quantify damage respectively. Numerical results show that the location and severity of the cracking damage can be successfully identified using only one sensor deployed on the bridge, which provides technical support to damage detection of cracks on the concrete simply-supported bridge.