In the presented work, the Klein-Fock-Gordon (KFG) equation is solved by the Nikiforov-Uvarov (NU) method for some spherically symmetric potentials: a linear combination of Hulthen and Yukawa class potentials, as well as a linear combination of Manning-Rosen plus Yukawa class potentials, by reducing it to a hypergeometric equation in quantum mechanics. Finding optimal solutions of wave equations for arbitrary values of theorbital quantum number l≠0 in such potential fields is considered one of the urgent problems of theoretical physics. As a result, analytical expressions for the energy spectrum, eigenfunction and normalization constants at arbitrary values of orbital quantum number have been found from the solution of the KFG equation. It has been shown that the energy spectrum and eigenfunction depend on the choice of the orbital quantum number l. Also, the energy levels and corresponding normalized eigenfunctions are represented as a recursion relation in terms of the Jacobi polynomials for arbitrary l states. Futhermore, a closed form for the normalization constant of the wave functions is found.