In this article, we study the stability of black hole solutions found in the context of dilatonic Horava–Lifshitz gravity in (Formula presented.) dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a non-vanishing cosmological constant, our results suggest unstable behavior for large values of the scalar field mass.