With the rise of the Internet of Things (IoT), more and more devices are connected to the Internet and the most challenging issue will be security. For resource-constrained devices, applying a heavy asymmetric cryptography mechanism is not workable. However, a symmetric crypto-system is resource-efficient and can be applied. The robustness of a symmetric crypto-system is based on successful key management schemes. However, most proposed key management schemes either focus on static connected devices and do not consider addition of new devices and their mobility or fail to provide sufficient resilience to node compromising attacks. In fact, device additions are suited for applications that require a long time of existence. However, these applications are very sensitive to node compromising attacks. This paper presents a new random key pre-distribution scheme designed for networks of resource-constrained devices. The proposed scheme ensures full-healing when devices are compromised and supports device mobility. The comparison of our scheme with respect to other key pre-distribution solutions shows its efficiency