In this paper, we propose PathRakeTCP, a method to estimate available bandwidth even if there are firewalls on the communication path that reject UDP communication. PathRakeTCP is one of the so-called packet train methods that estimates the available bandwidth by transmitting multiple probing packets. Firewalls often allow TCP communication to pass through. PathRakeTCP can pass through the firewalls because the packet train is composed of TCP packets. Many conventional packet train methods use UDP packets, which allow precise control over the transmission timing of each probing packet. This is because precise transmission timing control is essential for accurate available bandwidth estimation. On the other hand, if a packet train of TCP packets is simply transmitted, the transmission timing of each probing packet will be disrupted by TCP congestion control. This is a new problem not encountered in the conventional methods that use UDP packets. To solve the above problem, PathRakeTCP establishes a TCP connection for each probing packet and transmits only one packet at each TCP connection. To demonstrate that PathRakeTCP can precisely control the transmission timing of each TCP packet, an experimental evaluation is conducted with a real testbed. The experimental results show that the estimation error of PathRakeTCP is comparable to that of the packet train method with UDP packets.