Rich spectra of solar-like oscillations obtained with space observations are expected to enable us to perform precise determinations of stellar properties. To make the best of the spectra, we need theoretical stellar models with precise near-surface structure, since the near-surface structure has significant influence on solar-like oscillation frequencies. The mixing-length parameter, α, is a key factor to determine the near-surface structure. We aimed at determining appropriate α values based on 3D radiation-coupled hydrodynamical models produced by the CO^5BOLD code. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. The trends of the calibrated α values in the T_eff-g plane is found to be similar to those of previous calibrations with the other grids of RHD models. A T(τ) relation based on the so-called VAL-C solar-atmosphere model is found to give better correspondence to the photospheric-minimum entropy in the 3D model than the Eddington T(τ) relation. Although the structure below the photosphere depends on convection models, not a single convection model gives the best correspondence to the 3D model since physical quantities in the 3D models are not necessarily related via an equation of states unlike those in the 1D models. Although the FST model with a form of a mixing length (l=r_top-r+α^*H_p,{top}) is found to give solar-oscillation frequencies apparently closest to the observed ones, the acoustic cavity of this model is formed with compensatory effects between deviating density and temperature profiles just below the top of the convective envelope. In future work, a more sophisticated treatment of the top part of the 1D convective envelope is necessary.