The effect of the phase lag of temperature gradient, TT, on the transmission-reflection phenomenon, induced by a pulsed thermal energy passing the interface of a two-layered structure, within the framework of dual-phase-lag based heat conduction equation is studied numerically by the lattice Boltzmann (LB) method. An extended LB equation, with truncation error of order two, and a numerical solution procedure are developed for the solution of the governing equation and the derived interfacial boundary condition. Results show that the interface reflects a negative followed by a positive waveform when the pulsed thermal wave propagates from the media with lower TT into the media with higher TT and vice versa if the wave propagates from higher into lower tau(T) media. These special phenomena which have not been presented in the available literatures are unable to be predicted in the framework of hyperbolic heat conduction equation.