Introducing the mobility to Wireless Sensor Networks (WSNs) puts new challenges in designing an energy-efficient routing. Improving the network lifetime and the packet delivered rate are the most important issues in designing of the Mobile Wireless Sensor Networks (MWSNs). MWSN is more difficult to deal with than its stationary counterpart because it does not have a fixed topology. This increases the complexity of routing due to the frequent link breaks between clusters and their members. Various clustering protocols are developed to support mobility of the nodes in the WSNs. However, these protocols suffer from some limitations in connectivity, energy-efficient, fault tolerance, load balancing and mobility adaption because they organize the network into fixed size clusters and select the heads of these clusters randomly. Thus, this paper proposes an Adjustable Range-Based Immune hierarchy Clustering protocol (ARBIC) with mobility supporting to deliver the sensory data of the MWSN to the base station in an efficient way for a long-time. The operation of ARBIC protocol depends on organizing the network into optimum clusters and adjusting the size of these clusters based on the speed of the mobile sensor nodes to preserve the cluster connectivity. ARBIC protocol utilizes the immune optimization algorithm to determine the best positions of the clusters’ heads that optimize the trade-off among the mobility factor, energy consumption, connectivity, residual energy and link connection time. In order to save the overhead packets and the computational time, the ARBIC protocol runs the clustering process if and only if the residual energy of any cluster head is less than a predefined energy threshold. Moreover, it performs a fault tolerance mechanism after sending each frame to reduce the packets drop rate by maintaining the stability of links between the clusters’ heads and their member nodes. Mathematical analyses are established to analyze the computational and overhead complexities of the ARBIC protocol. Simulation results show that, compared with other protocols, the ARBIC protocol can effectively improve the packet delivery ratio while simultaneously offering lower energy consumption and delay by using sensor nodes with adjustable transmission ranges.