While wave heights globally have been growing over recent decades, observations of their regional trends vary. Simulations of future wave climate can be achieved by coupling wave and climate models. At present, wave heights and their future trends in the Arctic Ocean remain unknown. We use the third-generation wave forecast model WAVEWATCH-III forced by winds and sea ice concentration produced within the regional model HIRHAM, under the anthropogenic scenario SRES-A1B. We find that significant wave height and its extremes will increase over different inner Arctic areas due to reduction of sea ice cover and regional wind intensification in the 21st century. The opposite tendency, with a slight reduction in wave height appears for the Atlantic sector and the Barents Sea. Our results demonstrate the complex wave response in the Arctic Ocean to a combined effect of wind and sea ice forcings in a climate-change scenario during the 21st century. Key Points Significant wave height will increase over the Arctic Ocean in the 21st century Reduction in wave height is expected for the Atlantic sector and the Barents Sea ©2014. American Geophysical Union. All Rights Reserved.