We study the Holder regularity of weak solutions to the evolutionary p-Laplacian system with critical growth on the gradient. We establish a natural criterion for proving that a small solution and its gradient are locally Holder continuous almost everywhere. Actually our regularity result recovers the classical result in the case p = 2 [16] and can be applied to study the regularity of the heat flow for in-dimensional H-systems as well as the in-harmonic flow. (C) 2014 Elsevier Inc. All rights reserved.