Based on the economics theory of market, it is proposed that the brand competition is imperfect, the differentiation of which is the result of competition and one of the determinant factors of the firm's profit. The theory of random variable distribution is applied to quantitively analyze the relationship between the probability distribution of consumers' preference and their utility and demand for brands. The conclusion is that the differentiation of consumers' preference influences the market demand for brands through prices, thus the brands should be differenced if the firms want maximum market share. Also the relationship between firms' profits and the degree of brand competition differentiation is studied with the Shaked and Sutton model, and the result is the same if the firms want the more profits.