The tunneling current through a quantum dot array (QDA) is studied theoretically. Strong electron correlation effect is taken into account in the QDA in which the quantum dots provide a strong three-dimensional confinement effect. A mixed Hubbard and Anderson model is used to simulate the system. It is found that Coulomb charging splits the band resulting from interdot coupling into two subbands. The tunneling current is thus influenced significantly by both Coulomb charging and interdot coupling.