We establish a new class of three-point methods for the computation of simple zeros of a scalar function. Based on the two-point optimal method by Ostrowski (1966), we construct a family of order eight methods which use three evaluations of f and one of f′ and therefore have an efficiency index equal to (Formula presented.) and are optimal in the sense of the Kung and Traub conjecture (Kung and Traub J. Assoc. Comput. Math. 21, 634–651, 1974). Moreover, the dynamics of the proposed methods are shown with some comparisons to other existing methods. Numerical comparison with existing optimal schemes suggests that the new class provides a valuable alternative for solving nonlinear equations.