A turbine blade of a gas turbine includes a radially extending airfoil with a suction side and pressure side, which extend each in axial direction between a leading edge and a trailing edge of the airfoil. The leading edge is cooled by means of impingement cooling with rows of radially distributed jets of a cooling medium impinging on the inner side of the leading edge. The row of radially distributed jets is generated at an internal web, which divides the hollow interior of the airfoil into first and second cavities, with the second cavity being arranged at the leading edge. An enhanced cooling is achieved by the internal web that includes two rows of radially distributed cooling medium supply holes, through which cooling medium enters the second cavity in form of impinging jets. The cooling medium supply holes are oriented such that the directions of the jets of one row cross the directions of the jets of the other row.