In this paper, we study the following gradient system on a complete Riemannian manifold M, $\left\{\begin{matrix} -x'(t) = grad \phi(x(t))\\ x(0) = x_0 \end{matrix}\right.$, where ϕ : M → R is a C -1 function with Argminϕ ∅. We prove that the gradient flow x(t) converges to a critical point of ϕ if ϕ is pseudo-convex, or if ϕ is quasi-convex and M is Hadamard. As an application to minimization, we consider a discrete version of the system to approximate a minimum point of a given pseudo-convex function ϕ.