The transient stability preventive estimation and control is one of the most important tasks of the power system. The traditional time domain simulation method cannot meet the standard of on-line estimation because of its heavy computation burden. In this paper, we realize the on-line estimation of transient stability limits on critical lines of a power system using the favorable approximation ability of RBF network. We choose right samples by off-line count to train the RBF network in order to make the error satisfy demand. Preventive control direction and amount are determined based on first-order sensitivities of transient stability limits to generator outputs. The sensitivities are derived from partial derivatives of RBF network outputs to inputs. In the end, we take a practical power system for an example to demonstrate the efficiency of RBF network in estimation of the transient stability limit on critical lines and ability to provide preventive control strategy.