Lattice Boltzmann method is employed to study nonlinear heat conduction problems.A kind of lattice Boltzmann model is derived in details and multi-scale algorithm and macroscopic quantity are selected.It is proposed to solve transient responses of nonlinear heat conduction problems.The relation between heat conductivity and temperature meets the multi-polynomial function.Different parameters are considered to verify feasibility of the proposed method.Simulation results are illustrated with comparison in linear case.