The D-dimensional Klein-Gordon (KG) wave equation with unequal scalar and time-like vector Cornell interactions is solved by the Laplace transform method. In fact, we obtained the bound state energy eigenvalues of the spinless relativistic heavy quarkonium systems under such potentials. Further, the stationary states are calculated due to the good behavior of wave functions at the origin and at infinity. The statistical properties of this model are also investigated. Our results are found to be of great importance in particle physics.