Boolean function plays an important role in the design and analysis of symmetric cryptography. Firstly, by studying the balanced property of subfunctions of the disjoint spectra function set, some sufficient conditions were provided that there were three balanced Boolean functions in the set of four plateaued functions. Then, based on three balanced disjoint spectra plateaued functions, a special Boolean permutation and a balanced Boolean function with high nonlinearity, a method of constructing balanced Boolean functions with high nonlinearity was proposed on a small number of variables. The analysis results show that the proposed method can construct the 2 k-variable balanced Boolean functions with the optimal algebraic number and the nonlinearity is not less than 2 ^2k-1-2 ^k-1-2 ^k/2-2 ^{⌈(k-1)/2⌉}.