Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a medium bowl, cream together the shortening, white sugar and brown sugar until smooth. Beat in the egg and vanilla. Combine the flour, cocoa, baking soda and salt; gradually stir into the creamed mixture. Fold in the grated zucchini. Drop by rounded spoonfuls onto the prepared cookie sheets.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.