Recent development in Cloud and networking technologies have stimulated unification of network and Cloud service provisioning, in which service composition plays a crucial role. While encouraging progress has been made toward network-Cloud service composition, the impact of correlated network and Cloud services on the QoS of composite services, however, has not been sufficiently studied. In this paper, we address the challenging problem of QoS correlation-aware network and Cloud service composition. Specifically, we formulate this problem as a multi-constraint optimal path problem and propose a novel algorithm to solve it. We also evaluate the performance of the proposed algorithm with extensive simulations. The experimental results show that the proposed algorithm is effective and efficient and it is able to yield service composition solutions with better QoS guarantees through considering QoS correlations among different services.