We present the results of a study of light-light and heavy-light quark bound states by solving the Bethe-Salpeter equation, in which the non-perturbative part of the kernel is calculated up to four dimensions vacuum condensates in QCD in the background fields. We believe that it is a good approximation to neglect higher dimension vacuum condensates since we only deal with the ground states for 0- mesons. Indeed, satisfactory results (spectrum and decay constants) are obtained with reasonable parameters. In particular, we get an approximate relation f(P) is-proportional-to 1/square-root M(P) for the heavy-light quark mesons numerically.