The paper under review is concerned with a classification of Enriques surfaces with finite automorphism group over an algebraically closed field in positive characteristic, where the surfaces are assumed to have a smooth \(K3\) cover, in other words, they are in odd characteristics or singular Enriques surfaces in characteristic \(2\). For classical and supersingular Enriques surfaces in characteristic \(2\), see [T. Katsura et al., “Classification of Enriques surfaces with finite automorphism group in characteristic \(2\)”, Preprint, arXiv:1703.09609]. In this paper, the author classifies such Enriques surfaces into seven types using their dual graphs by extending universal base change construction of complex Enriques surfaces given by Lemma 2.6 of S. Kondō [Jap. J. Math., New Ser. 12, 191–282 (1986; Zbl 0616.14031)] to the case of arbitrary characteristic. He also shows that for every type \(K\in\{\mathrm{I},\cdots,\mathrm{VII}\}\) there exists an Enriques surface over prime field \(\mathbb{F}_p\) of type \(K\) with Picard rank \(10\) if an Enriques surface of type \(K\) exists in characteristic \(p\). Further, as an application of the classification, the semi-symplectic automorphism group of an Enriques surface of each type is determined.