By using the matrix form of the Fues-Kratzer-type (FK) potential, V(r) = Z(Ohm)/r + A/r(2), three-body problems of two-electron atomic systems are solved with the PHGLP expansion method. The atomic wave functions psi(Ohm) are constructed in terms of generalized Laguarre polynomials (GLP) and potential harmonics (PH). The calculations of the ground-state energies of atoms from He to Si12+ are tabulated using Deng et al.'s procedure and also the effect of the new potential onto excited states of S-1 Li+ are illustrated. Then, we calculated excited state energies (n(1)S, n = 1-3) of the atoms from He to Si12+ with the FK potential. The present results are compared with other theoretical calculations. It is pointed out that convergences of our results are more rapid than the results of the pure Coulombic interaction, and, so, this article increases the efficiency of the calculation for atomic three-body systems. (C) 2002 Wiley Periodicals, Inc.