In this paper we consider quasi-normal modes of test scalar and electromagnetic fields in the background of a non-Schwarzschild black hole in the Einstein-Weyl gravity. We find the dependence of the modes on the new parameter p, which is related to the coupling constant alpha, for different values of the angular parameter l and show that when l is increasing, the frequencies tend to linear dependence on p. We have also examined the case of a massive scalar field for which we have shown that the arbitrarily long lived modes (called quasi-resonances) exist in the spectrum.