This paper discussed the stability of a thin elastic helical rod with noncircular cross section in relaxed state, i.e., the stability of a rod with intrinsic curvature and twisting. Based on the Kirchhoff's kinetic analogy,the dynamical equations of the elastic rod were expressed by the Euler's angles.Neglecting the small force of inertia caused by the linear acceleration,only the inertial effect of the rotation of the cross section was considered,which made the Euler's equations closed. We proved that the Lyapunov's stability condition in first approximation was satisfied for the helical rod in relaxed state in the spatial domain, as well as in the time domain. Therefore the extensive and stable existence of a thin elastic rod with helical configuration in the nature can be explained theoretically. It was also noticed that a helical rod with negative Poisson ratio can be unstable.