The uniqueness of meromorphic functions f and their differential polynomials, sharing one small function, was investigated. The uniqueness theorem for f and L(f) sharing a(z) was proved and some previous results were improved. Let f(z) be a non-constant meromorphic function, k be a positive integer, and a(z)(a(z)≢0) be a small function of f(z). If f-a and L(f)-a share 0 IM, and 10δ(0,f) + 8(k + 1)Θ(∞,f)> 8k + 17, then f≡L(f).