We use the cross-correlation between the thermal Sunyaev–Zeldovich (tSZ) signal measured by the Planck satellite and the luminous red galaxy (LRG) samples provided by the SDSS DR7 to study the properties of galaxy cluster and intra-cluster gas. We separate the samples into three redshift bins |$z_{1}=(0.16,\, 0.26)$|⁠, |$z_{2}=(0.26,\, 0.36)$|⁠, |$z_{3}=(0.36,\, 0.47)$|⁠, and stack the Planck y-map against LRGs to derive the averaged y-profile for each redshift bin. We then fit the stacked profile with the theoretical prediction from the universal pressure profile (UPP) by using the Markov Chain Monte Carlo method. We find that the best-fitting values of the UPP parameters for the three bins are generally consistent with the previous studies, except for the noticeable evolution of the parameters in the three redshift bins. We simultaneously fit the data in the three redshift bins together, and find that the original UPP model cannot fit the data at small angular scales very well in the first and third redshift bins. The joint fits can be improved by including an additional parameter η to change the redshift dependence of the model (i.e. |$E(z)^{8/3}\, \rightarrow \, E(z)^{8/3+\eta }$|⁠) with best-fitting value as |$\eta =-3.11^{+1.09}_{-1.13}$|⁠. This suggests that the original UPP model with less redshift dependence may provide a better fit to the stacked tSZ profile.