In this paper the coupled lattice Boltzmann model is developed for simulation of multi-step combustion mechanism of a methane jet diffusion flame. The lattice Boltzmann scheme employs the double-distribution-function model, one distribution function for solving flow field and another for temperature and species concentration fields. The density and temperature fields are coupled through low Mach number flow field. The solution parameters such as species properties and rate of chemical reactions adjust in every time step according to temperature and concentration of species variations. Using combustion mechanisms instead of one step fast chemistry reaction and considering effect of temperature and species concentration on solution parameters are the main advantages of the developed model. For validation of the model, a four-step reduced mechanism with six species is used for simulation of combustion in a methane jet diffusion flame configuration. Agreement between the present results and experimental data confirms that this scheme is also an efficient numerical method for more detailed combustion simulations.