Based on the linear superposition theory in quantum mechanics, a kind of multi-mode functional superposition state light field which is made up of distinct unsymmetry five different multi-mode functional coherent states is developed. By using the mutli-mode squeezing state theory, the properties of the generalized nonlinear equal-power higher-power sum-squeezing of a kind of multi-mode functional superposition state light field is studied in detail. It is found that, under certain conditions, the first or the second perpendicular phase component of the multi-mode functional superposition state ligh field can present any generalized nonlinear equal-power higher-power sum-squeezing effect which changes periodically.