In this paper, a dual band antenna is designed using fractal geometry. The paper presents a triangular sierpinski fractal antenna which gives higher bandwidth of 670MHz & 1070MHz at resonant frequencies of 10.89GHz & 15.92GHz respectively. So, the triangular patch is used in this fractal antenna which adds some extensive applications in wireless industry. The multiband and ultra wide band properties of antenna are due to their self similarity of fractal geometry while the space filling properties of antenna leads to the miniaturization of antenna. This antenna miniaturization and self similarity property of triangular fractal structure is used for reducing antenna size and for obtaining dual band resonance with high gain of 7.0954dB at 10.89GHz. The double substrate structure is used for obtaining the efficient radiation characteristics which also influences gain and bandwidth of fractal antenna. The fractal antenna is also miniaturized by introducing various iterative procedures in sierpinski fractal structure that is considered as an attempt which has been made to design an antenna of compact size and good radiation characteristics. © 2015 IEEE.