The classic economic theories always assume the firm's objective is to maximize profit.However, it is not true in reality: the realistic companies have different incentives to set multiple objectives, or the non-profit maximization objective. So in this paper, the authors assume the monopolists have the non-profit maximization objective funcation, that is, the objective is the combination of its profit and some other aim with different weights. They analyze the relationship of the firms' behavior or strategies, the relationship of the firms' aims, then discuss the firm's best response to its new objective and to its competitor. This paper specifies two kinds of multiple objectives. The first one gives some weight to the firm's own revenue, the other one takes some industrial profit level into consideration.