Characteristics of control system design using Universal Learning Network (U.L.N.) are that a system to be controlled and a controller are both constructed by U.L.N. and that the controller is best tuned through learning. U.L.N has the same generalization ability as N.N.. So the controller constructed by U.L.N. is able to control the system in a favorable way under the condition different from the condition of the control system in learning stage. But stability can not be realized sufficiently. In this paper, we propose a robust control method using U.L.N. and second order derivatives of U.L.N.. The proposed method can realize better performance and robustness than the commonly used Neural Network. Robust control considered here is defined as follows. Even though initial values of node outputs change from those in learning, the control system is able to reduce its influence to other node outputs and can control the system in a preferable way as in the case of no variation. In order to realize such robust control, a new term concerning the variation is added to a usual criterion function. And parameter variables are adjusted so as to minimize the above mentioned criterion function using the second order derivatives of criterion function with respect to the parameters. Finally it is shown that the controller constricted by the proposed method works in an effective way through a simulation study of a nonlinear crane system.