We use the linear programming method and Deza Theorem for intersection family to prove the upper bound of two-distance sets(also three-distance sets) in Hamming space. This problem comes from the paper, ”On the size of maximal binary codes with 2, 3, and 4 distances”[1], which has proven that the maximum size of two-distance sets in Hamming space is 1 . Before this research, there were no understandable methods for high school students. We are also unsatisfied with the upper bound, so we aim to reduce the value of the upper bounds in certain specified cases. By solving the system inequalities that come from the Krawchouk polynomial and adopting former results such as Deza theorem, we achieve the upper bounds for the cases including A(n, {1, 2}), A(n, {2, 3}), A{(n, {1, 2, 3}), A(n, {3, 6}) and A(n, {k, 2k}) for k is an odd integer. For general {d1, d2} cases, we prove that A(n, {d1, d2)}) ≤ 2 when {d1, d2} is a pair of odd numbers. Additionally, during this research, several properties of the Krawchouk polynomial are also revealed, which can be applied in future discussions.