In this paper, we quantitatively evaluate the performance of GridFTP operating with the existing TCP by using a mathematical analytic approach. GridFTP has the following mechanisms for solving the problems of the existing TCP. First, for accelerating the start-up in the TCP?s slow start phase and achieving high throughput in the TCP?s congestion avoidance phase, multiple TCP connections can be established in parallel. Second, according to the bandwidth-delay product of a network, the TCP socket buffer size can be adjusted between GridFTP server and client. However, in the literature, sufficient investigation has been performed neither on the optimal number of TCP connections, nor the optimal configuration of the TCP socket buffer size. Therefore, in this paper, by focusing on the number of TCP connections and the TCP socket buffer size, we quantitatively investigate the optimal parameter configuration of GridFTP, in particular, in terms of the number of TCP connections and the TCP socket buffer size.