A numerical investigation was implemented to evaluate the kinetic effects of hydrogen addition on the thermal characteristics of lean and stoichiometric premixed methane-air flames, on the basis of the detailed kinetic reaction mechanism GRI-Mech 3.0. The flame temperature profiles and the distributions of reactive species were predicted as a function of flame height by solving a freely propagating laminar premixed flame model. Some global properties of the premixed flame, i.e., the flame temperature gradient, the inner layer flame temperature, and the heat release rate, were estimated. Results showed that hydrogen enrichment in methane-air flames led to increases in the peak flame temperature, the peak temperature gradient, and the peak heat release rate, but a decrease in the inner layer flame temperature. Analyses of the interactions among heat release rates, radical production, and reaction progress rates were conducted. Analysis of the contribution of the heat release rate showed that the reactions concerning CH3 consumption consistently released a large proportion of heat, while significant contributions were found from the reactions of OH + H-2 double left right arrow H + H2O, H + O-2 + H2O double left right arrow HO2 + H2O, and H + HO2 double left right arrow 2OH, when hydrogen was added. The rates of radical production were computed on the basis of the predicted species profiles. It was suggested that OH and H were the two important radicals, which had significant relevance to the heat release in the hydrogen-enriched flame. The analyses of the formation pathway were conducted for OH and H. It was shown that radical H was mainly produced in the reactions OH + H-2 double left right arrow H + H2O and O + H-2 double left right arrow H + OH, and the dominant reactions contributing to the production of radical OH were O + H-2 double left right arrow H + OH, O + CH4 double left right arrow OH + CH3, and H + HO2 double left right arrow 2OH. The progress rates of these preceding reactions were compared. Numerical results indicated that hydrogen had its kinetic effects on methane-air flames through promoting the formations and consumptions of OH and H, and the dominant reactions in terms of the contribution to heat release were OH + H-2 double left right arrow H + H2O, H + O-2 + H2O double left right arrow HO2 + H2O, and H + HO2 double left right arrow 2OH.