Greece is a member of the Schengen Agreement and there are no border controls between countries that have signed and implemented this treaty – the European Union (except Bulgaria, Croatia, Cyprus, Ireland, Romania and the United Kingdom), Iceland, Liechtenstein, Norway and Switzerland.
Likewise, a visa granted for any Schengen member is valid in all other countries that have signed and implemented the treaty. But be careful: not all EU members have signed the Schengen treaty, and not all Schengen members are part of the European Union. This means that there may be spots of customs check points, but no immigration checks (travelling within Schengen but to/from a non-EU country) or you may have to clear immigration but not customs (travelling within the EU but to/from a non-Schengen country).
For citizens from E.U., USA, Canada, Australia, New Zealand a visa IS NOT required
For detailed regulations applied to your country, refer to the Greek Ministry for Foreign Affairs.