In this paper, we derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in a scale-free network. Different from non scale-free networks such as ER (Erdos and Renyi) random graph, the connecting probability between nodes is dependent on their node degrees in scale-free networks. Hence, scale-free networks are generally not easy to analyze. Fekete et al. have derived the average throughput of TCP flows in a scale-free network by limiting network topologies to a class of scale-free trees (i.e., Barabasi Albert) tree). Not only the average throughput of TCP flows but also distributions of their performance metrics are important for design and control of communication networks. In this paper, we therefore derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in a scale-free network. Similarly to Fekete's approach, we use the BA tree as the network topology. Dynamics of TCP flows and routers are modeled with fluid-flow models. By utilizing known analytical results (i.e., distributions of link betweenness and path length in BA trees), we derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in steady state.