A fuel injection system for an internal combustion engine, the fuel injection system comprising: injectors (20, 30) including needle valves; and an electronic control unit configured to: (i) execute partial lift injection and full lift injection with the injectors, the partial lift injection being injection during which the needle valve does not reach a fully-open state and the full lift injection being injection during which the needle valve reaches the fully-open state; (ii) operate the internal combustion engine in a partial lift injection region where the injection of a required injection amount of a fuel is shared by the partial lift injection and the full lift injection; and (iii) correct an injection amount of the full lift injection with an amount of correction (ΔQ) of the required injection amount when the required injection amount is corrected while the internal combustion engine is operated in the partial lift injection region, the injection amount of the partial lift injection being maintained even when the required injection amount is corrected, wherein the electronic control unit is further configured to; allow the injection amount of the full lift injection to be injected after division into a plurality of the partial lift injections when the injection amount of the full lift injection falls short of a lower limit value of the injection amount of the full lift injection due to the correction of the required injection amount, and adjust the total of the injection amounts of the respective partial lift injections by a difference (ΔQp) between the injection amounts when the injection amount difference arises between the injection amount of the full lift injection prior to the division and the total of the injection amounts of the respective partial lift injections following the division when the injection amount of the full lift injection is divided into the plurality of partial lift injections. injectors (20, 30) including needle valves; and an electronic control unit configured to: (i) execute partial lift injection and full lift injection with the injectors, the partial lift injection being injection during which the needle valve does not reach a fully-open state and the full lift injection being injection during which the needle valve reaches the fully-open state; (ii) operate the internal combustion engine in a partial lift injection region where the injection of a required injection amount of a fuel is shared by the partial lift injection and the full lift injection; and (iii) correct an injection amount of the full lift injection with an amount of correction (ΔQ) of the required injection amount when the required injection amount is corrected while the internal combustion engine is operated in the partial lift injection region, the injection amount of the partial lift injection being maintained even when the required injection amount is corrected, wherein the electronic control unit is further configured to; allow the injection amount of the full lift injection to be injected after division into a plurality of the partial lift injections when the injection amount of the full lift injection falls short of a lower limit value of the injection amount of the full lift injection due to the correction of the required injection amount, and adjust the total of the injection amounts of the respective partial lift injections by a difference (ΔQp) between the injection amounts when the injection amount difference arises between the injection amount of the full lift injection prior to the division and the total of the injection amounts of the respective partial lift injections following the division when the injection amount of the full lift injection is divided into the plurality of partial lift injections. (i) execute partial lift injection and full lift injection with the injectors, the partial lift injection being injection during which the needle valve does not reach a fully-open state and the full lift injection being injection during which the needle valve reaches the fully-open state; (ii) operate the internal combustion engine in a partial lift injection region where the injection of a required injection amount of a fuel is shared by the partial lift injection and the full lift injection; and (iii) correct an injection amount of the full lift injection with an amount of correction (ΔQ) of the required injection amount when the required injection amount is corrected while the internal combustion engine is operated in the partial lift injection region, the injection amount of the partial lift injection being maintained even when the required injection amount is corrected, wherein the electronic control unit is further configured to;