Deploying a group of mobile sensor (MS) nodes to monitor a moving phenomenon in an unknown and open area includes a lot of challenges if the phenomenon moves quickly and due to the limited capabilities of MS nodes in terms of mobility, sensing and communication ranges. To address these challenges and achieve a high weighted sensing coverage, in this paper, we propose a new algorithm for moving-phenomenon monitoring, namely VirFID-MP (Virtual Force (VF)-based Interest-Driven phenomenon monitoring with Mobility Prediction). In VirFID-MP, the future movement of the phenomenon is first predicted using the MS nodes' movement history data. Then, the prediction information is used to calculate a virtual force, which is utilized to speed up MS nodes toward the moving phenomenon. In addition, a prediction-based oscillation-avoidance algorithm is incorporated with VirFID-MP movement control to reduce the nodes' energy consumption. Our simulation results show that VirFID-MP outperforms original VirFID schemes in terms of weighted coverage efficiency and energy consumption.