Visa Overstays Penalties Act This bill increases the civil penalties for unlawful entry into the United States and establishes criminal penalties for overstaying a visa. A non-U.S. national ( alien under federal law) apprehended while unlawfully entering the United States shall be subject to a fine of at least $500 and up to $1,000 (currently at least $50 and up to $250). If an individual overstays a visa (or otherwise fails to comply with the conditions of a visa) for 10 days or more, on first offense the individual shall be subject to fines or imprisonment for up to six months, or both. For subsequent violations, the individual shall be subject to fines or imprisonment of up to two years, or both.