Adaptive assistance of gait training robots has been determined to improve gait performance through motion assistance. An important control role during walking is to avoid tripping by controlling minimum toe clearance (MTC), which is an indicator of tripping risk, to avoid its decrease among gait cycles. No conventional gait training robots can adjust assistance timing based on MTC. In this paper, we propose a system that applies force intermittently based on the MTC prediction algorithm to encourage people to avoid lowering the MTC. This prediction algorithm is based on a radial basis function network, the input data of which include the angles, angular velocities, and angular accelerations of the hip, knee, and ankle joints in the sagittal and coronal planes at toe-off. The cable-driven system that can switch between assistance and non-assistance modes applies force when the predicted MTC is lower than the mean value. Nine participants were asked to walk on a treadmill, and we tested the effect of the system. The MTC data before, during, and after the assistance phase were analyzed for 120 s. The results showed that the minimum and first quartile values of MTC could be increased after the assistance phase.