The principle of the superconducting vortex flow transistor (SVFT) is based on control of the Abrikosov vortex flowing along a channel. The induced voltage is controlled by a bias current and a control current, instead of external magnetic field. The device is composed of parallel weak links with a nearby current control line. We explained the process to get an I-V characteristic equation and described the method to induce the external and internal magnetic field by the Biot-Savarts law in this paper. The equation can be used to predict the I-V curves for fabricated device. From the equation we demonstrated that the current-voltage characteristics were changed with input parameters. I-V characteristics were simulated to analyze a SVFT with multi-channel by a computer program.