This paper reports an object tracking algorithm for a moving platform using the dynamic and active-pixel vision sensor (DAVIS). It takes advantage of both the active pixel sensor (APS) frame and dynamic vision sensor (DVS) event outputs from the DAVIS. The tracking is performed in a three step-manner: regions of interest (ROIs) are generated by a cluster-based tracking using the DVS output, likely target locations are detected by using a convolutional neural network (CNN) on the APS output to classify the ROIs as foreground and background, and finally a particle filter infers the target location from the ROIs. Doing convolution only in the ROIs boosts the speed by a factor of 70 compared with full-frame convolutions for the 240x180 frame input from the DAVIS. The tracking accuracy on a predator and prey robot database reaches 90% with a cost of less than 20ms/frame in Matlab on a normal PC without using a GPU.