A turbine blade with a blade tip cooling passage formed within the blade tip and extending from the leading edge to the trailing edge. The blade tip passage includes a plurality of fins extending from the pressure side to the suction side walls of the passage, and in which each fin includes a cooling air opening, the openings of which alternate from the pressure side to the suction side in the passage to force the cooling air to flow in a sinusoidal manner. The openings also alternate from the bottom of the passage to the top of the passage so that the cooling air flows in a spiral shape manner. Film cooling holes are positioned along the pressure side walls for some of the spaces formed between adjacent fins to provide film cooling for the blade. A leading edge cooling supply channel supplies cooling air to the blade tip passage through a metering and impingement hole in the first space of the passage located on the leading edge. The fins with the alternating pattern of openings produce both impingement cooling and vortex cooling for the blade tip.