Preheat oven to 350 degrees F (175 degrees C). Grease an 11x7 inch baking pan.
In a medium bowl, beat sugar, oil, eggs, and vanilla until light and fluffy. Combine the flour, baking powder, salt, and cocoa; stir into the sugar mixture. Blend in the peanut butter. Spread batter evenly into the prepared pan.
Bake for 25 to 30 minutes in the preheated oven, until edges of brownies start to pull away from the sides of the pan. Cool before cutting into bars and serving.