Many non-equilibrium heat conduction processes can be described by the macroscopic dual-phase lag model (DPL model). In this paper, a numerical method. which combines the dual reciprocity boundary element method (DRBEM) with Laplace transforms, is constructed to solve such mathematical equation. It is used to simulate the non-Fourier phenomenon of heat conduction ill a single-phase medium. then numerically predict the differences between the thermal diffusion. the thermal wave and the non-Fourier heat conduction under different boundary conditions including pulse for one- and two-dimensional problems. In order to check this numerical method's reliability. the numerical solutions are still compared with two known analytical solutions.