A Schengen Visa (issued by a consulate or embassy of a Schengen State) is valid for all 26 States of the Schengen Area (including the European territory of Greece), unless it is marked otherwise on the visa sticker. So you do not need another visa to enter or stay in the European territory of Greece. However, you must be in possession of documentary evidence for the reasons of your stay and your means of support. Schengen Area comprises of the following countries: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, and Switzerland.