Preheat the oven to 325 degrees F (165 degrees C). Grease cookie sheets.
In a large bowl, cream together the shortening and sugar until light and fluffy. Add the egg, beat well, then stir in the vanilla and pineapple. Combine the flour, baking powder, baking soda and salt; gradually stir into the creamed mixture. Drop by rounded spoonfuls onto the prepared cookie sheet.
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.