In structural health monitoring (SHM), smartphones are increasingly used for non-contact dynamic displacement measurement using computer vision. To overcome limitations in capturing high-frame-rate data, a non-contact measurement method of structural dynamic displacement based on an improved edge detection algorithm and video frame interpolation is proposed. Initially, a smartphone is employed to capture the structure’s vibration video and then generates intermediary frames between adjacent frames that match the structure’s motion state by using a video frame interpolation algorithm to obtain a video with a high frame rate. Subsequently, the improved edge detection algorithm is applied to measure the displacement within the interpolated video. In order to address the problem that traditional edge detection may have false edges leading to the degradation of measurement accuracy, a feature point tracking technique is proposed based on the traditional edge detection technique, which effectively excludes the interference of false edges in ROI and improves the accuracy of displacement monitoring. Experimental validation on a cantilever beam and steel frame bridge demonstrates the method’s viability and precision, highlighting its effectiveness in improving displacement measurement accuracy compared to traditional methods.