It is a challenging work to develop efficient routing protocols for Delay Tolerant Mobile Sensor Networks (DTMSNs), which have several unique characteristics such as sensor mobility, intermittent connectivity, energy limit, and delay tolerability. In this paper, we propose a new routing protocol called Minimum Expected Delay-based Routing (MEDR) tailored for DTMSNs. MEDR achieves a good routing performance by finding and using the connected paths formed dynamically by mobile sensors. In MEDR, each sensor maintains two important parameters: Minimum Expected Delay (MED) and its expiration time. According to MED, messages will be delivered to the sensor that has at least a connected path with their hosting nodes, and has the shortest expected delay to communication directly with the sink node. Because of the changing network topology, the path is fragile and volatile, so we use the expiration time of MED to indicate the valid time of the path, and avoid wrong transmissions. Simulation results show that the proposed MEDR achieves a higher message delivery ratio with lower transmission overhead and data delivery delay than other DTMSN routing approaches.