Abstract: A class of Boolean functions f with suboptimal（or optimal） algebraic immunity is presented，by means of the second construction methods，a new class of Boolean functions h with optimal immunity is gotten.The h is different from what have been constructed before.The number of the functions f is given，the nonlinearity of the function h is discussed in the case of even number variables.Finally，the nonlinearity is discussed and that the nonlinearity of the function h constructed by means of the majority function F_n can make the Lobanov bound tight is found.