Abstract: Point reactor kinetic equations with six groups of delayed neutrons are solvedby use of the expansion of neutron population density and delayed neutronprecursors in forms of Laguerre Polynomials. The reactivity insertion into reactoris permitted to vary in time such as from zero to second powers. Under thecondition of constant reactivity insertion, the derived coefficient determinant witha tri--angle form is convenient to be solved. For the reactivity insertion varied intime, the forward--backward formula are derived so as to save calculation timein the higher order approximations. At last, the comparisons of results with thoseof the exact method as well as weighted residue method are shown to be satisfac-tory.