Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10-inch tube pan; line with parchment paper.
Combine sugar and butter in a large bowl; beat with an electric mixer until light and creamy. Beat in eggs one at a time, beating well after each addition. Add vanilla extract. Beat in peanut butter slowly.
Sift flour, baking powder, and salt together in a bowl. Mix into the butter mixture, a little at a time, until batter is well blended. Pour batter into the prepared tube pan.
Bake in the preheated oven until golden, about 45 minutes. Sprinkle peanuts on top. Reduce oven temperature to 325 degrees F (165 degrees C). Continue baking until a toothpick inserted into the center comes out clean, 15 to 20 minutes more.
Cool cake in the pan for 10 minutes. Invert onto a wire rack and let cool completely.