There exists a vast amount of methane-based combustible gases in the earth, such as natural gas, coalbed gas and shale gas. Usually there are non-combustible gases such as nitrogen in them and their combustion properties vary with composition. The knowledge on burning velocity and flame stability of those gaseous fuels is in great demand in order to achieve their efficient usage in industry and transportation. When measuring flame speed of an outwardly propagating spherical flame, the conventional analysis method assumes a linear relationship between flame speed and stretch rate. However, recent studies showed that the linear assumption could bring in errors when calculating unstretched flame speeds and Markstein lengths. In this study, we investigate laminar flame of methane/nitrogen and air mixtures by using a constant volume combustion chamber together with high-speed schlieren photography system. The experimental data have been analyzed by using both conventional method and nonlinear method that considers the effect of the stretch nonlinearly. Comparison shows that different methods do not affect flame speed results greatly, but have significant impact on Markstein length. Therefore nonlinear stretch effect should be considered. In this paper, unstretched laminar burning velocity and Markstein length of nitrogen diluted methane obtained by using nonlinear method are reported. The data covers a wide range of nitrogen diluted methane fuels whose nitrogen volume fraction varying from 0% to 50% at an interval of 10%. The effects of nitrogen concentration on laminar burning velocity and flame stability are then studied at different equivalence ratios (0.6-1.2). A correlation has been summarized for laminar burning velocity of methane/nitrogen and air mixtures obtained by using nonlinear analysis in this study.