The mass gaps existing in the discovered single heavy flavor baryons are analyzed, which show some universal behaviors. Under the framework of a constituent quark model, we quantitatively explain why such interesting phenomenon happens, when these established excited heavy baryons are regarded as the lambda -mode excitations. Based on the universal behaviors of the discussed mass gaps, we may have three implications including the prediction of the masses of excited Xi _b^0 baryons which are still missing in the experiment. For completeness, we also discuss the mass gaps of these rho -mode excited single heavy flavor baryons.