Fractal antenna designs can meet most of the needs in size reduction of antenna design. In this paper, Koch iteration technique is applied to a dipole antenna in order to get a miniaturized radar array element. The dipole antenna with 3rd Koch iteration applied to each of its four segments is designed to operate at a resonant frequency of 500 MHz. The four fractal segments of this antenna spin around the center axis with an angle difference of 90 degrees each, which results to an all-four-direction feature. The overall size of this dipole fractal antenna at the resonant frequency is reduced by around 33% compared with conventional dipole antenna meanwhile retaining its band characters. An improved model is also introduced with a better performance in bandwidth, which can reach more than 12% at 500 MHz.