Yes, Green Card holders (permanent residents of the United States) generally need to apply for a Schengen Visa to travel to Europe. The Schengen Visa is required for citizens of countries that are not exempt from the visa requirement.
Although Green Card holders have the right to live and work in the United States, they still hold the nationality of their home country. As a result, if their home country is not exempt from the Schengen Visa requirement, they must obtain a Schengen Visa to travel to the Schengen Area, which includes most European Union member states and certain non-EU countries.
It’s important to note that visa requirements can vary depending on your specific circumstances, including your nationality and purpose of travel. It is recommended to check the visa requirements of the particular Schengen country you plan to visit or consult with the embassy or consulate of that country for the most up-to-date and accurate information regarding visa requirements.