Non-Fourier heat conduction models assume wave-like behavior does exist in the heat conduction process. Based on this wave-like behavior, thermal conduction controlled in a one-dimensional periodical structure, named thermal wave crystal, has been demonstrated through both theoretical analysis and numerical simulation based on the Cattaneo-Vernotte (CV) heat-conduction model. The transfer matrix method and Bloch theorem have been applied to calculate the complex dispersion curves of thermal wave propagating in thermal wave crystals. And the temperature responses are obtained by using the FDTD method. The results show that the band gaps with pronounced heat reduction do exist in non Fourier thermal transfer process because of the Bragg scattering. The mid-gap frequency is well predicted analytically based on the Bragg scattering mechanism. Finally, the key parameters determining the band gaps are presented and discussed. This study shows the potential applications of these materials in heat isolation and reduction. (C) 2017 Elsevier Ltd. All rights reserved.