To suppress knock for improving thermal efficiency (ηth) of spark ignition (SI) engines, external exhaust gas recirculation (EGR) has been used. However, the use of EGR reduces flame speed, which leads to observed increase of cycle-to-cycle variations of SI combustion. To overcome this problem by reforming the fuel to add reactive compounds such as H2 and CO to the intake charge, dedicated EGR (D-EGR) concept is proposed, which uses a portion of the cylinders of a multi-cylinder engine to produce the entirety of the EGR consisted mainly of H2 and CO. To maximize the potential of D-EGR and provide new insights for improving ηth of SI engines, this study computationally investigates the use of D-EGR over a wide range of fuel-air equivalence ratios in four-cylinder engine (one D-EGR cylinder and three normal cylinders) for stoichiometric and lean operation. For the computations of laminar burning velocity (SL) and burned gas temperature (Tb), PREMIX in CHEMKIN-PRO were conducted with GRI-Mech 3.0 which is a detailed chemical-kinetic mechanism for methane (CH4).The results show that for D-EGR cylinder, both SL and Tb decrease with an increase of fuel/air equivalence ratios at D-EGR cylinder (ϕD-EGR) because the lower O2 as the more fuel is supplied to D-EGR cylinder for higher ϕD-EGR. ηth at D-EGR cylinder (ηth_D-EGR) decreases from 34.8% to 15.0% with an increase of ϕD-EGR from 1.0 and 3.0, regardless of changes in the amount of gross indicated work (Wg_D-EGR) and heat transferred to the combustion chamber (Qc_D-EGR) at D-EGR cylinder. For stoichiometric combustion at normal cylinder (ϕNormal = 1.0), both SL and Tb increase almost linearly with an increase of ϕD-EGR in the ϕD-EGR = 1.0–2.4 range. Furthermore, ηth at normal cylinder (ηth_Normal) increases from 34.8% to 51.9% between ϕD-EGR = 1.0 and 3.0. As a result, ηth of four-cylinder engine (ηth_Engine) with one D-EGR cylinder and three normal cylinders increases with an increase of ϕD-EGR, and the highest ηth_Engine (39.4%) is achieved for ϕD-EGR = 1.9. For lean combustion at normal cylinder (ϕNormal = 0.9, 0.8, 0.7, 0.6, 0.5), the higher SL and Tb are observed for the higher ϕD-EGR, similar to stoichiometric combustion (ϕNormal = 1.0). Eventually, by a combination of D-EGR addition and lean combustion, the highest ηth_Engine of 42.9% is obtained for ϕNormal = 0.7 with ϕD-EGR of 2.0. This corresponds to a 16.0% increase of ηth_Engine relative to the baseline which is a stoichiometric charge consisted of CH4 and air without any EGR (ηth_Engine = 26.9%).