To improve the efficiency of full-spectrum correlated-k-distribution (FSCK), a new method FSCK-RSM has been proposed based on response surface methodology (RSM) in this paper. The k-distributions of FSCK was used to fit the response surface model based on radial basis function and the radiative calculation efficiency was improved by avoiding multiple computations and interpolation in the FSCK-RSM. The thermal radiation heat transfer of five combustion gases (H2O, CO2, CO, C2H2 and C2H4) in a one-dimensional layer was investigated and the radiative sources calculated by the LBL, SNB, FSCK and FSCK-RSM methods were given at different distributions of temperature and gas concentration. The results showed that the needed amount of input data was reduced by 677 times using FSCK-RSM comparing to the FSCK and the maximum of the average normalized deviation for FSCK-RSM was 2.46% in the non-isothermal homogeneous medium. The model was finally used for radiation reabsorption calculations in planar C2H4/O2/N2/CO2 flames with full coupling to heat transfer and multi-species chemistry. The computational time using the FSCK-RSM was found to be at most half of that using the FSCK method. This FSCK-RSM model was an effective method for addressing the radiation problems that occur in combustion systems.