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In recent years, Wireless Sensor networks (WSNs) have gained great attention and are composed of low power, resource constrained and short range communication devices are increasingly being adopted in different application scenarios including environmental monitoring, home and building automation, assisted living, logistics, transportation and industrial automation. In this context, mobility is becoming more important thus introducing new technological challenges also referring to security. The constrained devices should be protected from various security attacks and provided with secure data communication capabilities. To this aim, a proper key management scheme supporting mobility is required. In fact, a number of secure key management schemes have been proposed in literature only considering the static nature of sensor nodes. In this paper, we present a key management scheme supporting mobility in a heterogeneous WSN that consists of mobile sensor nodes with few fixed sensor nodes. In particular, the proposed solution addresses the minimization of required memory space, provides enhanced connectivity and network resilience against node capture attack compared to some existing schemes. We also proposed two levels of secure authentication methods for the mobile sensor nodes and the avoidance of replay attack and node replication attack.