In the year of 1991, Lin Achan established a theory about the approximation and saturation of Jackson polynomial under Hölder metric. On the basis of those results,Jackson polynomial has been approximated under the generalized Hölder metric by using metric definition, modulus property, and interpolation feature of Jackson polynomial combining with the method of magnifying or diminishing inequality, the theory is effective proved. The following question is solved, namely, for a norm of the subtraction between function and its corresponding Jackson polynomial under generalized Hölder metric attains the certain degree, what kind of condition function and its conjugate function have to satisfy? In the end, two results about approximation and saturation of Jackson polynomial under generalized Hölder metric are obtained, which is more extensive than quondam conclusion.