Recently, there have been exploratory growth in the research of wireless sensor network due to wide applications like health monitoring, environment monitoring, and urban traffic management. Sensor network applications have been used in habitat monitoring, border monitoring, health care, and military surveillance. In some applications, the security of these networks is very essential and need robust support. For a network, it is very important that node in the network trust each other and malicious node should be discarded. Cryptography techniques are normally used to secure the networks. Key plays a very important role in network security. Other aspects of security such as integrity, authentication, and confidentiality also depend on keys. In wireless sensor network, it is very difficult to manage the keys as this includes distribution of key, generation of new session key as per requirements, and renewal or revoke the keys in case of attacks. In this paper, we proposed a scalable and storage efficient key management scheme (SSEKMS) for wireless sensor networks that establish the three types of keys for the network: a network key that is shared by all the nodes in the network, a cluster key shared for a cluster, and pairwise key for each pair of nodes. We analysed the resiliency of the scheme (that is the probability of key compromise against the node capture) and compared it with other existing schemes. SSEKMS is a dynamic key management system that also supports the inclusion of the new node and refreshes the keys as per requirements.