The integral boundary value problem for a class of nonlinear fractional integro-differential equations with two fractional derivative terms is studied. Firstly, the original problem is transformed into an equivalent form with only one derivative term. The existence and uniqueness theorems of positive solutions of the original problem are established by defining the upper and lower solutions of the equivalent problem and using the monotone iterative technique. The iterative schemes and error estimates for finding the unique solutions are obtained. Finally, an example is presented to illustrate the effectiveness and potential applications of our main results.