Due to advances in high-speed radio access technologies (HS-RATs), such as 5G and WiGig, it will be possible for mobile users to use ultra-high-speed access services via user equipment (e.g., smartphones) in the 5G era. However, HS-RATs cannot provide wide coverage areas per base station because of high-frequency wave-band use. Operators have to install many HS-RAT base stations to provide widespread ultra-high-speed access services. Therefore, operators need to apply HS-RAT in combination with other RATs, such as Long Term Evolution (LTE), instead of deploying many base stations at an early stage of installing HS-RATs. We call this a multi-RAT environment, which consists of multiple RATs, such as HS-RAT and existing RAT. In this multi-RAT environment, when mobile users move around between LTE and HS-RAT areas, the bandwidth of mobile equipment will cause drastic fluctuation during communicating by establishing or disconnecting radio links between an existing RAT and HS-RAT cell. In this bandwidth fluctuation, mobile users cannot obtain the desired throughput immediately because of conventional TCP congestion control algorithms. In this paper, we propose bandwidth information based congestion control (BCC), a TCP congestion control algorithm, by using available-bandwidth information from base stations for maximizing throughput on a multi-RAT environment. We evaluated BCC by using the ns-3 simulation tool and network testbed with an actual Linux machine.