The notion of tree-shifts constitutes an intermediate class between one-sided shift spaces and multidimensional ones. This paper proposes an algorithm for computing the entropy of a tree-shift of finite type. Meanwhile, the entropy of a tree-shift of finite type is for some , where λ is a Perron number. This extends Lind's work (1984 Ergod. Theor. Dynam. Syst. 4 283–300) on one-dimensional shifts of finite type. As an application, the entropy minimality problem is investigated, and we obtain a necessary and sufficient condition for a tree-shift of finite type to be entropy-minimal with some additional conditions.