In the design of Internet of Things (IoT), sensor nodes are used in collecting data from an environment and sending it to a base station or sink for future processing. These sensor nodes have some resource constraints such as power supply. Hence, in order to prolong the network lifetime, we need to manage the energy consumption of these sensor devices. Thus, in this paper, a tree-based routing protocol is proposed that is efficient in power consumption and reduces the end-to-end delay in energy-efficient green-IoT networks with a mobile sink. Two new different mechanisms are introduced in the proposed protocol for managing the routing in the network. The first mechanism is an improved version of the geographic routing algorithm, which is more reliable and energy-balanced. The second mechanism is a tree-based structure that can be created with the minimum control packets and updated with an efficient procedure. Simulation results indicate that the proposed routing algorithm is superior to the existing ones in terms of energy consumption, network lifetime, delay, and throughput.