The helical instability of an arc column with electrical conductivity of the parabolic distribution and transparent radiation of the parabolic distribution is discussed in axial magnetic field.The magnetohydrodynamic equations serve as the strarting point of the theory.In an electrostatic approximation and a linear time dependent perturbation theory,the perturbation equations for the arc column movement are deduced.Solutions of these equations are obtained analytically,from which the stability limit of the cylindrical arc and the growth rate of the helical instability are given.In comparision the results with those of current distribution without radiation,it is found that the radiation in the small middle arc increases the instability.