In a small mixing bowl, cream the butter, peanut butter and sugars. Beat in egg and vanilla. Combine the flour, oats, baking soda and salt; gradually add to creamed mixture and mix well. Stir in Grape-Nuts.
Drop by rounded teaspoonfuls 3 in. apart onto ungreased baking sheets. Flatten slightly with a fork dipped in flour. Bake at 350° for 9-12 minutes or until lightly browned. Cool for 5 minutes before removing from pans to wire racks.