In this paper, we propose a wideband microstrip patch antenna for Ka-band CubeSat applications. A square patch antenna printed on a grounded FR4 slab is used as the building block. Furthermore, its performance is enhanced in terms of impedance bandwidth by adding a parasitic element close to the radiating edge of the main patch and by adding slots across the non-radiating edges of the patch to further improve the gain performance. A wide -10dB impedance bandwidth of 21% as well as a -3dB gain bandwidth of 35% across the Kaband were achieved. The antenna presents excellent cross polarization discrimination performance in the E-plane with a maximum gain of 7dBi at 28.3GHz.