Node compromising is still the most hard attack in Wireless Sensor Networks (WSNs). It affects key distribution which is a building block in securing communications in any network. The weak point of several roposed key distribution schemes in WSNs is their lack of resilience to node compromising attacks. When a node is compromised, all its key material is revealed leading to insecure communication links throughout the network. This drawback is more harmful for long-lived WSNs that are deployed in multiple phases, i.e., Multi-phase WSNs (MPWSNs). In the last few years, many key management schemes were proposed to ensure security in WSNs. However, these schemes are conceived for single phase WSNs and their security degrades with time when an attacker captures nodes. To deal with this drawback and enhance the resilience to node compromising over the whole lifetime of the network, we propose in this paper, a new key pre-distribution scheme adapted to MPWSNs. Our scheme takes advantage of the resilience improvement of Q-composite key scheme and adds self-healing which is the ability of the scheme to decrease the effect of node compromising over time. Self-healing is achieved by pre-distributing each generation with fresh keys. The evaluation of our scheme proves that it has a good key connectivity and a high resilience to node compromising attack compared to existing key management schemes.