We propose a new multipath routing protocol called DMR for mobile sensor networks, where any node can move anytime. DMR is based on the IETF RPL framework, which uses directed acyclic graph (DAG) to remove routing cycles. By broadcasting DAG construction messages including rank and link quality indication, DMR constructs DAG and provides path redundancy. This allows mobile sensors to find multiple alternative paths easily on local and global route failures. Our experimental results show that DMR successfully delivers more than 97% of messages while improving the energy efficiency for MSN by effectively reducing routing overheads by 65% and 56% on average compared to the existing MANET routing protocols AODV and AOMDV, respectively.