Line an 8-in. square pan with foil or parchment paper. Spray with cooking spray or grease with butter.
In a large saucepan, combine sugar and milk. Bring mixture to a rolling boil while stirring constantly. Boil for 3 minutes, then immediately remove from the heat.
Stir in peanut butter, marshmallow fluff and vanilla extract until combined. Spread into 8" pan and smooth the top with an offset spatula.
Refrigerate until firm, about 2 hours. Lift fudge out of pan, cut edges off to make all sides of the fudge smooth, then cut into squares. Store between layers of parchment or wax paper in an airtight container.
Storage: Store between layers of parchment or wax paper in an airtight container at room temperature. Fudge stays fresh for about a week.