We compute the quasinormal spectra for scalar, Dirac and electromagnetic perturbations of the Schwarzschild–de Sitter geometry in the framework of scale-dependent gravity, which is one of the current approaches to quantum gravity. Adopting the widely used WKB semi-classical approximation, we investigate the impact on the spectrum of the angular degree, the overtone number as well as the scale-dependent parameter for fixed black hole mass and cosmological constant. We summarize our numerical results in tables, and for better visualization, we show them graphically as well. All modes are found to be stable. Our findings show that both the real part and the absolute value of the imaginary part of the frequencies increase with the parameter ϵ that measures the deviation from the classical geometry. Therefore, in the framework of scale-dependent gravity the modes oscillate and decay faster in comparison with their classical counterparts.