The paper addresses the problem of online adaptive learning in a neuro-fuzzy network based on Sugeno-type fuzzy inference. A new learning algorithm for tuning of both antecedent and consequent parts of fuzzy rules is proposed. The algorithm is derived from the well-known Marquardt procedure and uses approximation of the Hessian matrix. A characteristic feature of the proposed algorithm is that it does not require time-consuming matrix operations. Simulation results illustrate application to adaptive identification of a nonlinear plant and nonlinear time series prediction.