Network traffic is growing at an outpaced speed globally. The modern network infrastructure makes classic network intrusion detection methods inefficient to classify an inflow of vast network traffic. This paper aims to present a modern approach towards building a network intrusion detection system (NIDS) by using various deep learning methods. To further improve our proposed scheme and make it effective in real-world settings, we use deep transfer learning techniques where we transfer the knowledge learned by our model in a source domain with plentiful computational and data resources to a target domain with sparse availability of both the resources. Our proposed method achieved 98.30% classification accuracy score in the source domain and an improved 98.43% classification accuracy score in the target domain with a boost in the classification speed using UNSW-15 dataset. This study demonstrates that deep transfer learning techniques make it possible to construct large deep learning models to perform network classification, which can be deployed in the real world target domains where they can maintain their classification performance and improve their classification speed despite the limited accessibility of resources.