Let f be a transcendental meromorphic function defined in the complex plane C and k ∈N. We consider the value distribution of the differential polynomial f q0 ( f (k))qk , where q0(≥ 2), qk(≥ 1) are integers. We obtain a quantitative estimation of the characteristic function T(r, f ) in terms of N ( r, 1/ f q0 ( f (k))qk−1 ) . Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., Vol. 14, PP. 93-100, 2011); Karmakar and Sahoo (Results Math., Vol. 73, 2018) for a particular class of transcendental meromorphic functions