Nuclear fuel rods are exposed to axial flow in a reactor, and flow-induced-vibration due to the flow usually causes damage in the fuel rods. Thus a prior knowledge about dynamic behavior of a fuel rod exposed to the flow condition should be provided. This paper shows that dynamic characteristics of a nuclear fuel rod depend on axial flow velocity. Assuming small lateral displacement, the effects of uniform axial flow are investigated. The analytic results show that axial flow generally reduces fuel rod stiffness and raises its damping in normal condition. Also, the critical axial velocities which make the fuel rod behavior unstable were found. That is, solving generalized eigenvalue equation of the fuel rod dynamic system, the eigenvalues with positive real part are detected. Based on the simulation results, on the other hand, it turns out that the ordinary axial flow in nuclear reactors does not affect to stability of a nuclear fuel rod even in the conservative condition.