Abstract Unstable minimal surfaces are the unstable stationary points of the Dirichlet integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used, an application of which was presented in [Struwe, J. Reine Angew. Math. 349: 1–23, 1984] for minimal surfaces in Euclidean space. We extend this theory to obtain unstable minimal surfaces in Riemannian manifolds. In particular, we consider minimal surfaces of annulus type.