Observational evidence shows a rising sea level in the last century and half in association to the elevated anthropogenic forcing. This rising sea is mainly contributed by the thermal expansion of the seawater in association to the absorption of the additional heat by the sea water, melting of the land-based ice (glaciers, ice caps and ice sheets) and the vertical motion of land. Here we analyzed two sets of large ensemble simulations to quantify the uncertainty of the regional sea level change due to thermal expansion induced by internal climate variability. Results show that different climate sensitivity can modulate the global mean and regional sea level rise by altering the amount of heat absorbed by the ocean. The response of internal variability, such as AMOC, to the rising anthropogenic forcing is capable to enhance and reduce the local sea level rise in regions where are strongly influenced by these internal variability.