Fuel supply system and method for delivering fuel to a fuel injector

A fuel supply system for a combustion engine (101) comprises a multitude of fuel injectors (106, 107, 108, 109) for providing fuel to the combustion engine (101) and a multitude of fuel pumps (110, 111, 112, 113) . Each fuel pump of the multitude of fuel pumps (110, 111, 112, 113) is hydraulically coupled with one fuel injector (106, 107, 108, 109) for providing fuel to the respective fuel injector (106, 107, 108, 109). The respective fuel pumps (110, 111, 112, 113) each comprise an electromagnetic or piezoelectric actuator for driving the respective fuel pump (110, 111, 112, 113). A Method for delivering fuel to the fuel injector (106, 107, 108, 109) of the combustion engine (101) comprises a controlling of a pump (110) to suck in fuel into a pump chamber when a fuel injector (106) that is hydraulically coupled to the pump (110) is in a closed state and a controlling of the fuel injector (106) to move to an open state as to inject the fuel of the pump chamber into a combustion chamber (102) of the combustion engine (101) , wherein the fuel out of the pump chamber is ejected out of the pump chamber only when the fuel is injected into a combustion chamber (102) via the fuel injector (106).