Abstract: Based on the importance of Maxwell fluids in various fields such as science, engineering and technology, and combined with the wide interest of non-Fourier heat conduction effects in many different research fields, the influence of non-Fourier effects on the thermal convection instability of Maxwell fluids in vertical channels is investigated in this paper. The non-Fourier heat transfer equation is obtained by adding a new transient term including the thermal relaxation time to the traditional Fourier heat transfer model. A generalized eigenvalue problem is numerically solved using the Chebyshev configuration method, and the temporal growth rate and neutral stability curve for each parameter are obtained. The results show that the temporal growth rate increases with the increase of the relaxation time parameter Λ. The neutral stability curve shows that the effect of relaxation time is almost negligible in the relatively small range of wave number. However, when the wave number increases, the effect of relaxation time on the convective instability is gradually intensified. This indicates that the elastic effect of Maxwell fluids enhances the thermal convection instability in vertical pipes. For Fourier fluids, the neutral stability curve does not vary with the Prandtl number. On the other hand, the non-Fourier effect enhances the convective instability, and the new hyperbolic heat transfer equation causes the neutral stability curve to fluctuate. Further studies show that this fluctuation is enhanced with the increase of Prandtl number. When the Prandtl number surpasses a specific critical value, the neutral stability curve splits into stationary and oscillatory branches. Furthermore, in the oscillatory branches, the instability is greatly increased.