A systematic procedure for the calculation of mesonic masses in QCD with large number of colors is proposed. The masses are expanded in terms of an auxiliary parameter α, which is set to 1 at the end of the calculation. The expansion coefficients are expressed in general in terms of the Feynman integrals of QCD. The terms of order αn involve diagrams with n loops. Explicit expressions are found up to α3. These terms appear to be rather small, so that one may try to extrapolate to α = 1. The qualitative properties of the spectrum are plausible, but for quantitative predictions further calculations are required.