In this work, by applying the redshift tomography method to Joint Light-curve Analysis (JLA) supernova sample, we explore the possible redshift-dependence of stretch-luminosity parameter α and color-luminosity parameter β. The basic idea is to divide the JLA sample into different redshift bins, assuming that α and β are piecewise constants. Then, by constraining the ΛCDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the same technique to explore the possible evolution of β in various subsamples of JLA. Using the full JLA data, we find that α is always consistent with a constant. In contrast, at high redshift β has a significant trend of decreasing, at ∼ 3.5σ confidence level (CL). Moreover, we find that low-z subsample favors a constant β; in contrast, SDSS and SNLS subsamples favor a decreasing β at 2σ and 3.3σ CL, respectively. Besides, by using a binned parameterization of β, we study the impacts of β's evolution on parameter estimation. We find that compared with a constant β, a varying β yields a larger best-fit value of fractional matter density Ω m0 , which slightly deviates from the best-fit result given by other cosmological observations. However, for both the varying β and the constant β cases, the 1σ regions of Ω m0 are still consistent with the result given by other observations.