In this paper, we consider the no-wait two-machine scheduling problem with convex resource allocation and learning effect under the condition of common due date assignment. We take the total earliness, tardiness and common due date cost as the objective function, and find the optimal common due date, the resource allocation and the schedule of jobs to make the objective function minimum under the constraint condition that the total resource is limited. The corresponding algorithm is given and proved that the problem can be solved in polynomial time.