The surface lattice resonance (SLR) created by metal nanoparticles in a regular periodic array shows a narrower bandwidth than single nanoparticles, leading to widespread applications in the field of nanolasers and nanosensors. In this work, we studied the plasmonic properties of the Ag trigonal-helix nanostructures (ATHNs). Our results show that an ultra-narrow Fano resonance with linewidths as narrow as ~1.5 nm from arrays of ATHNs at λ ~ 388 nm, which will be especially useful in the UV-applications. Moreover, the resonant wavelength of the Fano peaks shows a strong dependence on the array periodicity, which enables us to adjust Fano resonance at the desired wavelength in all UV-Vis and near-IR regimes. The results of this work may be used to build more advanced sensors based on the Fano plasmon lattice resonance.