There are some approaches for all-hexahedral mesh quality improvement by means of node-movement while preserving the connectivity. Among these methods, the most easily implemented and well known one is the Laplacian smoothing method; however, for this method mesh quality improvement is not guaranteed in all cases, and this approach might cause inverted elements especially in concave regions. In this work, a method for the improvement of hexahedral mesh shape-quality Without causing inverted elements is proposed; which is based on optimization of an objective function calculated by means of the individual qualities of hexahedral elements in the mesh. The shape-quality for each hexahedral element is defined via the condition number of the relevant element. The numerical optimization scheme is the particle swarm optimization method, which originated from observations related to the social behaviors of bird, insect, or fish colonies. The purpose of this paper is to discuss the applicability of this approach to mesh smoothing. Some examples are given in order to demonstrate the applicability. Copyright (C) 2008 John Wiley & Sons, Ltd.