This paper proposes a compact non-canonical non-uniform conformal phased array antenna (NNCPAA) attached to an irregular UAV surface to overcome the space and aerodynamic constraints for high-gain, wide-scan applications. The NNCPAA is parametrically determined using a geometric sequence for the x-axial spacings of array elements in the center rows to manipulate the elevation scan, while the y-axial spacings take care of the azimuth scan. It outperforms its equal-aperture uniform conformal counterpart before amplitude or phase synthesizing as it can achieve a lower sidelobe level, a smaller elevation-scan angle, and a wider 2D scanning coverage. Moreover, based on the proposed NNCPAA, a co-design method is developed for a compact high-performance onboard system at 5.8 GHz. By using improved miniature elements, the inter-element mutual coupling is reduced and all elements can be directly attached to the locally flat parts of the actual UAV surface, thus without any mechanical support added to the whole system. The experiments show that the onboard system achieves a peak gain of 21.8 dBi, a high efficiency of 88.4%, and scanning ranges exceeding 51° and ±28° with small scanning losses of 2.2 dB and 0.5 dB in elevation and azimuth, respectively. Therefore, the designed NNCPAA system is promising for UAV-based wireless communication (e.g., V2X) and remote sensing.