Analytical solutions of the position-dependent mass Klein-Gordon equation in the presence of unequal scalar and vector Yukawa potentials for arbitrary l-state are obtained by using the generalized parametric Nikiforov-Uvarov method. With an approximation scheme to deal with the centrifugal term, we get the bound state energy eigenvalues and the corresponding wave functions, expressed in terms of the Jacobi polynomials. Subsequently, we consider a special case for a = 0 and explicitly obtain the energy eigenvalues as well as the corresponding eigenfunctions in terms of the Laguerre polynomials. Some results are also compared with the previous studies.