In container terminals, the integrated planning of berth allocation and quay crane assignment problems has attracted much attention in literature. These problems can be integrated either by functional integration or by deep integration approaches. In the functional integration approach, these problems are integrated by being divided into two sub-problems and a feedback loop is used to interconnect them. A presumed vessel handling time is used for each vessel at first to initiate the integration mechanism. The functional integration approach achieves the required performance of each problem and is less complicated compared with the deep integration in which the two problems are merged into a unified model. However, the sensitivity of the solution to the assumed vessel handling time and the non-convergence to a stable state are the weak points of the functional integration approach. This paper presents a new functional integration approach for the following problems: berth allocation, quay crane assignment and specific quay crane assignment. Numerical experiments are conducted to test the performance of the proposed approach. The results illustrate that the proposed approach shows no sensitivity to the presumed handling time and a significant improvement in the convergence to stable state. Compared to a unified model from literature, the effectiveness of the proposed approach is investigated. In addition, by using actual container terminal data, the applicability of the proposed approach is demonstrated