Fast movement of objects and illumination changes may lead to a negative effect on camera images for object detection and tracking. Event cameras are neuromorphic vision sensors that capture the vitality of a scene, mitigating data redundancy and latency. This paper proposes a new solution to moving object detection and tracking using an event frame from bio-inspired event cameras. First, an object detection method is designed using a combined event frame and a standard frame in which the detection is performed according to probability and color, respectively. Then, a detection-based object tracking method is proposed using an event frame and an improved kernel correlation filter to reduce missed detection. Further, a distance measurement method is developed using event frame-based tracking and similar triangle theory to enhance the estimation of distance between the object and camera. Experiment results demonstrate the effectiveness of the proposed methods for moving object detection and tracking.