Nanowire photonic crystal (PhC) structure is one of promising approaches to enhance vertical light extraction efficiency (LEE) of ultraviolet light emitting diodes (UV LEDs). There are lots of investigations to study the structure of nanowire UV LEDs by using the finite-difference time-domain (FDTD) method. The optimal LEE are obtained by using some optimization algorithms. However, it needs a broad window, not the best values of geometrical parameters of nanowires in practical fabrication. In this paper, the vertical LEE of UV LEDs are theoretically enhanced by selecting the band gaps of AlGaN-based nanowire PhC structure. It illustrates that all the gaps can inhibit the horizontal propagation of light. However, the inhibiting ability of Gap 1 are weaker than them of Gap 2 and Gap 3.The reason is that the radii of nanowires in Gap 1 are too small to support enough guided modes. As a comparison, both Gap 2 and Gap 3 can efficiently inhibit the radiated mode propagation, and finally enhance the vertical LEE. In addition, the variations of height, number, and refractive index of nanowires on vertical LEE and optical band gaps are discussed. This work has benefits for the practical production of nanowire PhC UV LEDs.