Ocean warming is a key factor impacting future changes in climate. Here we investigate vertical structure changes in globally averaged ocean heat content (OHC) in high- (HR) and low-resolution (LR) future climate simulations with the Community Earth System Model (CESM). Compared with observation-based estimates, the simulated OHC anomalies in the upper 700 m and 2000 m during 1960-2020 are more realistic in CESM-HR than -LR. Under RCP8.5 scenario, the net surface heat into the ocean is very similar in CESM-HR and -LR However, CESM-HR has a larger increase in OHC in the upper 250 m compared to CESM-LR, but a smaller increase below 250 m. This difference can be traced to differences in eddy-induced vertical heat transport between CESM-HR and -LR in the historical period. Moreover, our results suggest that with the same heat input, upper-ocean warming is likely to be underestimated by most non-eddy-resolving climate models.