An estimation method based on empirical likelihood was proposed for a class of double-function coefficient autoregressive conditional heteroscedasticity-mean (ARCH-M) model. In this method, the proposed model allows the risk effect and return effect of financial time series to be the functional structure of a certain variable at the same time, which can effectively describe the relationship between the risk and average return of financial time series and has a wide range of adaptability. Meanwhile, compared with the classical moment estimation method and maximum likelihood estimation method, the estimation method based on empirical likelihood has unique advantages. This estimation method can fully consider the heteroscedasticity of financial series, and the constructed confidence interval does not involve any estimation of asymptotic variance, so it has better robustness and effectiveness. Under some regularity conditions, the asymptotic distribution of the constructed empirical log-likelihood ratio statistic and the estimator of function coefficients was analyzed theoretically. The results showed that the empirical log-likelihood ratio statistics about the risk effect function coefficient and the income effect function coefficient asymptotically converged to the central chi-square distribution, while the function coefficient estimator asymptotically converged to the normal distribution. Additionally, the point-by-poin confidence intervals of the corresponding function coefficients were constructed for the risk effect function coefficient and the income effect function coefficient, respectively.