In this paper, we discuss the unicity problem of certain shift polynomials. Suppose that cj (j = 1, …, s) be distinct complex numbers, n, m, s and μj (j = 1, …, s) are integers satisfying n + m > 4σ + 14, where σ = μ 1 + μ 2 + … μs . We prove that if and share ″(α(γ),0)″, then either or . The results obtained greatly improve the results of Saha (Korean J. Math. 28(4)(2020)) and C. Meng (Mathematica Bohemica 139(2014)).