Countering Violent Extremism Grants Act or the CVE Grants Act

Amends the Homeland Security Act of 2002 to authorize the use of Urban Area Security Initiative and State Homeland Security Grant Program funding to prevent, prepare for, protect against, and respond to acts of terrorism by countering violent extremism, including through: (1) training programs; (2) the development, implementation, or expansion of programs to engage communities that may be targeted by violent extremist radicalization; and (3) the development and implementation of projects to partner with local communities to prevent radicalization to violence.

Directs the Federal Emergency Management Agency (FEMA) to submit an annual report on the use of such funding to counter violent extremism, including a list of recipients of funds, the types of projects funded, and the amount of grant funding used for each project.