This paper presents a novel unequal power divider based on an inverted microstrip gap waveguide. This new geometry can achieve a large power ratio of the two output ports and a small phase difference less than 5°. Based on this novel geometry, a few distinctive unequal power dividers with different output power ratios were proposed for designing a low sidelobe array antenna at 39 GHz. To verify the design, a 16×16 antenna array was designed and measured. The measurement results indicate that the entire array antenna achieves a -10 dB impedance bandwidth of 18.5% (in the range of 35.9-43.2 GHz), a gain greater than 29 dBi from 37.5 to 41.8 GHz and an antenna efficiency greater than 50% over the entire operating frequency band. Based on the application of the newly invented distribution network, the proposed array antenna is below -23 dB on both the E-and H-planes at 37-42 GHz. Furthemore, the radiation pattern of the entire array complies with the ETSI-Class II standard for all azimuth angles.