In this paper, a symmetrically feeding structure for linear dual-polarized feeds for a compensated compact test range (CCR) and a corresponding wideband balun are put forward. $TM_{01}$ and $TE_{21} $ modes within the circular feeding waveguide are compressed due to its electrical balance. The polarization purity of feeds is then improved. Thus, the level of cross-polarization can be very low, which is the key requirement for CCR. A new wideband balun that acts as a power-divider and phase shifter with low amplitude unbalance and phase unbalance is designed for the new feeding structure. The return loss equation derived from an equivalent microwave network for this symmetric structure is different from the ordinary single port feeding structure. In low frequency range applications, reflection at the interface between the coaxial and circular waveguide can reach a high level; a transition probe is designed to depress it. VSWR is reduced from 2.25 to 1.85 with two specially designed rectangular holes on the ground plane of the balun, while amplitude unbalance is less than $\pm $0.15 dB and phase unbalance is less than $\pm $0.5$^{\circ}$. Simulation results show that VSWR and cross-polarization performances of symmetric feeding feeds are both better than those of a dual-polarized quadruple-ridged horn.