The energy eigenvalues and eigenfunctions of the Sehrodinger equation for Eckart potential as well as the parity-time-symmetric version of the potential in three dimensions with the centrifugal term are investigated approximately by using the Nikiforov-Uvarov method. To show the accuracy of our results, we calculate the energy eigenvalues for various values of n and l.It is found that the results are in good agreement with the numerical solutions for short-range potential (large a).For the case of l/a(→)i/a, the potential is also studied briefly.