The remarkable progress in wireless communication system and an increasing demand to integrate different technologies into the small user equipment has given a rise to the fashion of introducing compact multiband antennas. In addition to the size reduction and multiple frequency characteristics, further challenge for antenna design engineers is to optimize the antenna for performance i.e., wide bandwidth, high gain, reduced return loss, omnidirectional radiation pattern, low cross polarization and reduced cost for fabrication. The advent of Koch curve fractal antenna has enabled the engineers to meet up these challenges easily without compromising on size. Moreover, the space filling property of Koch curve monopole antenna is an added advantage over conventional wired dipole and monopole antennas. In this paper two novel antennas, based on the Koch curve fractal geometry are proposed. Moreover parametric study on the surface current distribution on these antennas is also included in this paper. These compact Koch curve monopole patch antennas are designed by applying third iterative transformation to the straight wire monopole. Further, the height of one antenna was reduced by bending the 2/3 pattern of the Koch monopole antenna counter clockwise. Then, again rotating the whole antenna 900 counter clockwise. Both antennas are fed by 3 mm transmission lines and the frequencies of operation for the proposed antenna #1 and antenna #2 are 2.45 and 5 GHz ISM (Industrial scientific medical) bands. The proposed antennas have some favourable characteristics such as; compact size almost symmetrical radiation patterns, multiband characteristics, satisfactory return loss; less than -10 dB and acceptable bandwidth in desired frequency bands. © 2010 IEEE.