We design, fabricate and characterize a plasmonic honeycomb lattice absorber with almost perfect absorption at 1140 nm over a wide incident angle range. This absorber also possesses a narrow-band, angle- and polarization-dependent high-order resonance in the short-wavelength range, with a bandwidth of 19 nm and angle sensitivity of 3 nm per degree. The nature of this high-order absorption band is analyzed through finite-element simulations. We believe it is due to Bragg coupling of the incident light to the backward-propagating surface plasmon polariton through the periodic modulation of the structure.Such fine absorption bands can find applications in plasmonic sensors and spectrally selective thermal emitters.