A pump for a liquid cosmetic product dispenser including a body defining a metering chamber provided with an admission orifice at the bottom and having an opening at the top into which is inserted a sleeve carried by an axially movable operating head which is provided with a delivery duct and an open/close element and is acted upon by a return spring mounted on the outside of the body. The body encloses a jacket that moves axially inside the chamber and at least partly inside the sleeve and supports a lower valve for closing the admission orifice.