The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on the acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagation in a fluid-filled borehole is demonstrated based on the generalized Biot–Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in the time domain. The results are also compared with those based on generalized Biot’s theory. The results show that the influence of non-Newtonian effects on acoustic guided waves, especially on the attenuation coefficients of guided waves propagation in borehole is noticeable.