The group asked to meet with the governor and then vowed to stay in Scott's office overnight when they were told he wasn't there. Scott's schedule shows that he is in New York City.
Protesters say they want Scott to call a special session and ask state legislators to change laws that they say harm blacks.
One they want repealed is the state's "stand your ground" law that allows people to use deadly force if they believe their life is in danger.
Zimmerman shot 17-year-old Trayvon Martin, who was unarmed, during a February 2012 confrontation in Sanford, Fla. Zimmerman said he fired his gun in self-defense.
A six-member jury on Saturday cleared Zimmerman of all charges in Martin's death.
Ciara Taylor from Jacksonville said the group was "standing our ground for Trayvon, for justice."
The protesters first gathered on the steps of the historic Capitol building, then went over to Scott's office.
It marks the second time that there has been a protest at the state Capitol since the verdict was announced. Roughly 200 protesters assembled at the Capitol early Sunday morning.
During last year's outcry over Martin's death, it was Scott who created a task force to look at the state's self-defense laws.
That task force ultimately recommended this past February that the state's "stand your ground" law works and should not be overturned. The group did recommend that standards for neighborhood watch groups should be looked at by the Legislature.
Some legislators recommended making changes to the law, but those bills went nowhere this past session in the Republican-controlled Legislature.