This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomials of moromorphic functions in this paper. In particular, we are interested in the existence of zeros of $f(z)^n({lambda}f(z+c)^m+{mu}f(z)^m)-a$, where f is a moromorphic function, n, m are two non-negative integers, and ${lambda}$, ${mu}$ are non-zero complex numbers. However, the proof here is obviously different to the one in [9]. We also study difference polynomials of entire functions sharing a common value, which improves the result in [10, 13].