A corporate feeding antenna array with parasitic patches has been investigated previously for millimeter-wave applications due to its high gain and wide bandwidth. However, the parasitic patch integration in the uniformly powered and spaced patch antenna array led to a high sidelobe level (SLL). In this study, we designed a non-uniformly powered and spaced corporate feeding network to feed a 12-element parasitic patch-integrated microstrip antenna array for SLL reduction at 28 GHz in the millimeter-wave band. In the power divider, we arranged two one-to-six unequally feeding power dividers from the opposite side to feed 12 antenna elements with non-uniform excitation, and effectively controlled the spacing between antenna elements. The two opposite input ports from the power divider were fed 180° out-of-phase for good isolation between the adjacent antenna elements. To verify the SLL reduction effect from the non-uniform spacing in the array, we designed two non-uniformly powered patch antenna arrays with uniform and non-uniform spacing. In the measurement, the non-uniformly powered and spaced patch antenna array demonstrated a nearly 16.56 dBi boresight gain and −17.27 dB SLL, which is nearly 2 dB lower than the uniformly spaced counterpart. Finally, we expect that the non-uniformly powered and spaced high gain patch antenna array with a low SLL will be suitable for millimeter-wave communication applications.