GPUs have become important solutions for accelerating scientific applications. Most of the existing work on climate models now use code rewritten using CUDA to achieve a limited speedup. This restriction also greatly limits followup development and applications. In this paper, we designed and implemented a GPU-based acceleration of the LASG/IAP climate system ocean model (LICOM) version 2, called LICOM2-GPU. Considering the extremely large codebase of the model and the occasional need to modify the code, we implemented the model completely in OpenACC. Several accelerated methods, including OpenACC data locality optimization, loop optimization, and interprocess communication optimization are presented. Developing for GPUs using OpenACC is substantially simpler than using the CUDA port. Thus, the OpenACC is a suitable GPU programming model for complex systems, such as the earth system model and its components. Our experimental results using 4 NVIDIA K80 cards achieved up to a 6.6$ \times $ speedup compared with 4 Intel(R) Xeon(R) CPU E5-2690 v2 GPUs.