Internet of things (IoT) is a network of smart things. This indicates the ability of these physical things to transfer information with other physical things. The characteristics of these networks, such as topology dynamicity and energy constraint, challenges the routing problem in these networks. Previous routing methods could not achieve the required performance in this type of network. Therefore, developers of this network designed and developed specific methods in order to satisfy the requirements of these networks. One of the routing methods is utilization of multi-path protocols which send data to its destination using routes with separate links. One of such protocols is AOMDV routing protocol. In this paper, this method is improved using gray system theory which chooses the best paths used for separate routes to send packets. To do this, AOMDV packet format is altered and some fields are added to it so that energy criteria, link expiration time, and signal to noise ratio can also be considered while selecting the best route. The proposed method named RMPGST-IoT is introduced which chooses the routes with highest rank for concurrent transmission of data, using a specific routine based on the gray system theory. In order to evaluate and report the results, the proposed RMPGST-IoT method is compared to the ERGID and ADRM-IoT approaches with regard to throughput, packet receiving rate, packet loss rate, average remaining energy, and network lifetime. The results demonstrate the superior performance of the proposed RMPGST-IoT compared to the ERGID and ADRM-IoT approaches.