The mobile network operators are moving towards Virtual Network Functions (VNFs), in place of traditional dedicated hardwares for the 5G deployment. The VNFs require low maintenance and give high flexibility compared to dedicated hardwares which are prone to failures. Typically, VNFs are run on top of Virtual Machines (VMs) which run on physical nodes in data centers. For each class of service, based on its policy, the traffic has to pass through a set of VNFs in sequence termed as Service Function Chains (SFCs). Selection of available VNFs to steer the SFC requests with guaranteed end-to-end latency is still an open problem. In this work, we design an algorithm named DAVIS (Delay-Aware VNF selectIon algorithm for SFC) to increase the SFC acceptance rate by efficiently selecting VNFs. Simulation results show that DAVIS improves the throughput of accepted requests by 42% while guaranteeing SLA requirements. © 2019 IEEE.