The influence of different melting time of Greenland ice sheet on sea level of the global and regional oceans were studied using the ocean model parallel ocean program (POP) under the representative concentration pathway 4.5 (RCP 4.5) scenario for the 21st century. Results showed that the Greenland ice sheet melting with 7%*a~(-1) acceleration in the year round has more notably influence on the global and regional sea level variation than melting only in the summer months from May to October. The dynamic sea level rise shows acceleration in the Arctic and subpolar North Atlantic, but it decreases in the west coast of Europe and subtropical North Atlantic. The steric sea level rises fast along the coast of North America, subpolar North Atlantic, tropical Atlantic, and the subtropical South Atlantic, but falls in the Arctic, the west coast of Europe and subtropical North Atlantic. The different influences of the Greenland ice sheet melting on sea level change between the year round and the summer months cases mainly due to the notably weakened meridional overturning caused by strengthened stratification of the upper ocean and weakened deep convection because of a lot of freshwater input regions near Greenland in the high rate of melting Greenland ice sheet. The accumulation of water in the subpolar North Atlantic caused by weakened meridional overturning, which leads to dynamic sea level rise in the subpolar North Atlantic. The weakened transport of heat and salt from the tropical Atlantic to high-latitude ocean was caused by weakened meridional overturning, so that more high temperature and saline water was stranded in the tropical Atlantic; part of high temperature and high salinity water was brought by the Gulf Stream to the Gulf Stream region, leading to accelerated thermosteric sea level rise and significant halosteric sea level decrease in the Gulf Stream and tropical North Atlantic. The waters of the subpolar North Atlantic and Arctic cool and become less saline, some cold and less saline water was brought by the wind-driven circulation to the subtropical North Atlantic, which led to opposite change of thermosteric and halosteric sea level to tropical North Atlantic.