The stability of a helical vortex tube is studied by short-wavelength stability analysis. The ratio € of the core to the curvature radius is assumed to be small but finite. The base flow of the helical vortex tube is obtained by perturbation expansion which exhibits rotational and translational motions as a whole. It is shown that the helical vortex tube is subject to curvature instability, which was first found for the vortex ring. The growth rates of the curvature instability are obtained both analytically and numerically. The effects of torsion and rotation are investigated. Both torsion and rotation appear as second-order correction to the growth rate of the curvature instability which is first order in €. They break symmetry so that the maximal growth rates are larger than the vortex ring of which all the parameters but torsion and rotation are the same.