The experimental measurements and computational predictions of the laminar burning velocity of DME and methane blends with air are reported in the present work. The well documented and validated rectangular diverging channel was used for the measurements. Whereas, one dimensional freely propagating flame simulations were performed using PREMIX code detail reaction mechanisms. The measured experimental data and predictions were successfully validated against the data available at ambient conditions. Then, high temperature burning velocity measurement and predicted data is reported. Influence of mixture equivalence ratios, blend combinations, and initial temperatures are critically analysed and discussed. The detail flame structure variation is also reported with the help of heat release rates, major and minor species profiles, reaction pathways, sensitivity analysis, and fake/pseudo-specie analyses. The addition of DME into methane enhances the reactivity and burning velocity. However, the rate of increase in burning velocity with respect to an increase in initial temperature is higher for pure methane + air mixtures.