The optimal differentially private mechanism problem is to maximize the data utility on a fixed privacy protection extent. The optimal mechanism problem is an important topic in differential privacy, which has close connection with both theoretical foundation and future applications of differential privacy model. This paper proposes a analyzing method about the topic, which is not based on the sensitivity method. First, the optimal mechanism problem is constructed to be a multi-objective optimization problem, and a new method for constructing differentially private mechanism is introduced. Then, a near-optimal mechanism is provided for the linear queries, which reaches the boundary of the differential privacy inequality. Although this paper focuses on the linear queries, most part of the analyzing method introduced is applicable to the non-linear queries. This paper finds the drawback of the sensitivity method and uncovers some deeper characteristics of differential privacy.