Fourier law can be solved by means of the classical Lattice Boltzmann Method (LBM) with Bhatnagar-Gross-Krook (BGK) collision operator. However, classical LBM is challenged in the microscale conduction. In present work, we proposed a new collision operator based on Dual Phase Lag (DPL) model, a generalized conduction law, and developed an Expanded Lattice Boltzmann Method (ELBM). To validate our derivation, a numerical example is presented. It is found that the results predicted by the ELBM coincide with the analytical solutions of DPL model quite well. ELBM has a simpler differential form than other classical simulation methods. (C) 2015 Elsevier Ltd. All rights reserved.