This paper studies local rigidity for some isometric toral extensions of partially hyperbolic Zk (k ≥ 2) actions on the torus. We prove a C∞ local rigidity result for such actions, provided that the smooth perturbations of the actions satisfy the intersection property. We also give a local rigidity result within a class of volume preserving actions. Our method mainly uses a generalization of the Kolmogorov-Arnold-Moser iterative scheme.