Yes, the GDPR does apply to individuals. If you process or collect the data of EU residents, you’re required to comply with the GDPR — regardless of whether you’re a business, organization, or individual.
However, according to Article 2 of the GDPR, the GDPR does not apply to individuals if they collect personal information as a “purely personal or household activity.” For example, an individual with an address book with the names and phone numbers of EU residents is not subject to comply with the GDPR.