A compact dual-band Wilkinson power divider (WPD) using the via-free dual-composite right/left-handed (D-CRLH) resonators is presented for application in the Beidou navigation satellite system in this brief. First, by establishing an equivalent circuit model and using Bloch theory, a dual-band resonator is further analyzed to gain insight into its working mechanism, which can exhibit −90° phase shift at lower frequencies and +90° phase shift at upper frequencies, respectively. Then, to facilitate the design, ignoring parasitic parameters, a simplified circuit model retaining the physical meaning is presented, and the closed-form formulas for determining lumped element values of a dual-band characteristic are derived. Next, there is a significant rejection performance between two operating frequencies due to the inherent band-stop filtering effect of the D-CRLH resonator. Following that, the WPD is verified through experiments, showing excellent performance. Finally, based on this property, a dual-band feeding network (FN) is constructed by the combination of a WPD and a phase shifter with the proposed resonator. The simulated and measured results are found in good agreement with each other, which further demonstrated our proposed design conception.