Flow correlation is a crucial task for operators to efficiently manage data center networks, as it provides a holistic perspective of the data center network by correlating ingress flow at each network node with the corresponding egress flow on a hop-by-hop basis. Existing attempts to solve the flow correlation problem involve traditional and feature-based methods, which have major limitations in application scenarios, processing speed and accuracy in the dynamic data center network environment, especially at the presence of chains of Virtual Network Functions (VNFs). Addressing this issue, this paper proposes a novel deep neural network based flow correlation method, called DeepMetricCorr. DeepMetricCorr composes multidimensional flow statistical features, metric learning, and a channel attention mechanism to solve flow correlation problems accurately. It is featured with a lightweight design which reduces computational overhead. The experiments on real-world datasets demonstrate that DeepMetricCorr outperforms other state-of-the-art methods in correlation accuracy, especially on load balancers with an over 2× improvement. Furthermore, the model maintains a low latency (¡0.5 s) as the number of candidate flows increases over 8000.