A fast and accurate novel design method is proposed for the design of broad omnidirectional bandgaps of one dimensional (1-D) photonic crystals (PCs). Presented method is verified with various numerical examples for 1-D photonic crystals which consist of a cascade of two quasi-periodic stacks and broad omnidirectional bandgaps are achieved. Furthermore, computation time requirement of the presented method is considerably less than that required for purely numerical approaches. The proposed algorithm is quite flexible and can easily be modified to address problems involving 1-D PCs consisting of three and more cascaded stacks and specific 2D PC structures. (C) 2014 Elsevier GmbH. All rights reserved.