The Nikiforov-Uvarov method is employed to calculate the any 1-state solutions of the Schrodinger equation for a diatomic molecular system in the rotating Morse potential. The bound state energy eigenvalues and the corresponding eigenfunctions are obtained by applying the Pekeris approximation to the centrifugal barrier term of the potential. All of these calculations present an effective and methodological procedure under the Pekeris approximation and Nikiforov-Uvarov method to solve the rotating Morse system. In addition, the results obtained here are shown to be in good agreement with the numerical data and results from the other approximations and methods. (c) 2005 Elsevier B.V. All rights reserved.