Preheat oven to 350 degrees F (175 degrees C). Grease a 9 inch springform pan.
In a medium bowl, mix together graham cracker crumbs, 1/4 cup sugar and melted butter. Press mixture into the bottom of the prepared pan.
In a large bowl, beat cream cheese until smooth. Gradually beat in 1 1/4 cups sugar until blended. Beat in eggs one at a time, then stir in vanilla and sour cream.
Pour filling into prepared crust. Bake in preheated oven for 45 minutes. Turn off oven and let cake cool inside for one hour. Remove from oven and cool completely.
Chill cheesecake in refrigerator overnight before serving.