Network Function Virtualisation (NFV) aims to increase the deployment flexibility and integration of new network services with increased agility within operator’s networks. Due to the promises of NFV, it is also considered as one of the building blocks for 5G and edge computing. However, the Intrinsic dynamic features of NFV and even rigorous requirements proposed by 5G and edge computing expose severe challenges to resource management in NFV. In this paper, We study the problem of Virtualised Network Function (VNF) chain placement in dynamic environment, and formulate it as Integer Linear Programming problem with taking the dynamic characteristics of resource allocation into consideration. Then we propose an efficient dynamic algorithm with provable competitive performance based on primal-dual approach combined with an efficient subroutine. The theoretic analysis shows our algorithm is $(1 - 1/e)$-competitive to offline optimal solution. Finally, We evaluate the proposed approach through extensive numerical simulations. Experiment results show that the proposed algorithm achieves near-optimal competitive ratio and has much better performances than several algorithms in many aspects.