In the Community Earth System Model (CESM), the ocean model is computationally expensive for high-resolution grids and is often the least scalable component for high-resolution production experiments. The major bottleneck is that the barotropic solver scales poorly at high core counts. We design a new barotropic solver to accelerate the high-resolution ocean simulation. The novel solver adopts a Chebyshev-type iterative method to reduce the global communication cost in conjunction with an effective block preconditioner to further reduce the iterations. The algorithm and its computational complexity are theoretically analyzed and compared with other existing methods. We confirm the significant reduction of the global communication time with a competitive conver- gence rate using a series of idealized tests. Experimental results obtained with the CESM 0.1◦ global ocean model show that the proposed approach results in a factor of 1.7 speed-up over the original method with no loss of accuracy, achieving 10.5 simulated years per wall-clock day on 16,875 cores.