The non-relativistic Schrödinger equation of electron plus hydrogen-atom system is solved by the Hulthén type variational method at the limit of zero incident electron energy. 8 and 5 parameter trial functions are used for the singlet and triplet states respectively, and the following upper bounds on the scattering length a are obtained, as ≦6.217a0 (singlet), at ≦2.272a0 (triplet). Some discussions are given on the accuracy of the result. It is shown that the relation aOH > aSH > aK > a (true) holds for trial functions of the same form if a(true) is positive.