In the paper, we study the value distribution of the differential polynomial Af ⁿ fᵏ + Bf ⁿ+¹ − 1 where f is a transcendental meromorphic function and n(≥ 2), k(2) are positive integers. We prove an inequality for the Nevanlinna characteristic function T(r, f) in terms of reduced counting function only. The result of the paper not only improves the result due to Q.D. Zhang [J. Chengdu Ins. Meteor., 20(1992), 12-20], also partially improves a recent result of H. Karmakar and P. Sahoo [Results Math., (2018),73:98]