In this paper a star fish shaped microstrip patch antenna is proposed and its design procedure and characteristics are analyzed. The shape of the antenna patch is similar to a star fish, therefore the antenna is called Star fish antenna. The proposed antenna is able to provide dual band operation in V band (40-52 GHz) and W band (77-95 GHz) which lie in the range of millimeter wave frequency. The proposed antenna has 8 branches of unequal length in order to achieve wide bandwidth in millimeter wave range. Each of the branch resonates at different frequency which ultimately results in a wide bandwidth of 30 GHz with an efficient gain of 7.9026 dBi and highly reduced return loss. Designed antenna has a very compact dimensions of 9×9×2.03 mm ³ , thus it can be easily fabricated with small handset devices.