With the exponential growth in the number of mobile devices, providing Internet access via WiFi in trains is rapidly becoming a necessity. Cellular network is predominantly used for the backhaul connection to the train. However, the railway companies of developing countries may not go for cellular-network-based solutions mainly for two reasons: (1) high deployment cost of a cellular network and (2) lack of sufficient coverage of existing cellular networks of telecom companies along the railway tracks. In this paper, we propose a Software Defined Networking (SDN)-based architecture to provide Internet connectivity inside trains. The backhaul connection to the train, in the proposed architecture, is provided via WiFi. Deployment of such an architecture is more cost-efficient than that of a dedicated cellular network of the same capacity, or that of the existing cellular networks of telecom companies, since there are no running tariffs and the spectrum is free. Moreover, this architecture can be used to provide connectivity in the coverage holes of the existing networks of the telecom companies. Through simulation, we show that the architecture can provide high throughput and packet delivery ratio while maintaining per packet delay within reasonable limits inside a train.