Four implicit potential energy surfaces (PESs) with specific-reaction-parameters (SRP) are developed and tested for the reaction CH4 + H → CH3 + H2. The first is called MPW60 and is based on the modified Perdew-Wang (mPW) hybrid density-functional method with the percentage of Hartree-Fock (HF) exchange equal to 60%. The other three PESs are constructed with multi-coefficient correlation methods (MCCMs). The second is called MCOMP2-SRP, and the third is called MC-QCISD-SRP. Both of them are parameterized for this specific reaction by starting with their corresponding global parameters (GP). The fourth is called MCG3-SRP and is based on the MCG3-CHO semiglobal parameterization (SGP) with further refinement for this specific reaction. All four SRP surfaces have a classical forward barrier height of 14.8 kcal/mol, and all three MCCM SRP surfaces have a classical endoergicity of 3.3 kcal/mol. The stationary point geometries, vibrational frequencies, and zero-point-energies (ZPEs) are reported for several standard single-level methods and MCCMs with global parameters as well as for the four new SRP surfaces. Direct dynamics calculations are carried out using variational transition state theory (VTST) with multidimensional tunneling contributions on the proposed SRP surfaces. We calculate forward reaction rate constants for the title reaction from 250 to 2400 K and compare them with the latest re-analyzed experimental results over the temperature range from 348 to 1950 K. The calculated rate constants using canonical variational theory with the small-curvature tunneling approximation (CVT/SCT) carried out on the MPW60, MC-QCISD-SRP, and MCG3-SRP surfaces show good agreement with the experimental results.