This paper studies evolutionary programming with mutations based on the Lévy probability distribution. The Lévy probability distribution has an infinite second moment and is, therefore, more likely to generate an offspring that is farther away from its parent than the commonly employed Gaussian mutation. Such likelihood depends on a parameter in the Lévy distribution. We propose an evolutionary programming algorithm using adaptive as well as nonadaptive Lévy mutations. The proposed algorithm was applied to multivariate functional optimization. Empirical evidence shows that, in the case of functions having many local optima, the performance of the proposed algorithm was better than that of classical evolutionary programming using Gaussian mutation.