The time delay factor has an important influence on the solution of the fractional differential system. The change of the system solution not only depends on the current state, but also is constrained by the past state. Therefore, it is of great significance to consider the delay effect in the fractional differential system. In this paper, the existence and uniqueness of solutions for a class of boundary value problem of fractional order differential equation with delay are disscussed. Firstly, the equivalent equation of fractional order differential equation with delay is given by constructing the Green function and the relevant properties of the fractional calculus. Then, the problem of solving this equivalent equation is transformed into a fixed point problem in Banach space. By applying Banach contraction mapping principle and Schauder fixed point theorems, some sufficient conditions ensure that the uniqueness and the existence of solutions of boundary value problem for fractional order differential equation with delay are obtained respectively. Finally, two examples are presented to verify the theoretical results. In this paper, we use a special norm in Banach space to obtain sufficient conditions for the existence and uniqueness of the solution of the system, which is simpler than the previous results. This method is novel and can be used to discuss the existence and uniqueness of positive solutions for boundary value problems of fractional Langevin equations with time delay.