As metallic nanoparticles are arranged to form a 2D periodic nano-array, the coupling of the localized surface plasmonic resonance (LSPR) results in the well-known phenomenon of surface lattice resonances (SLRs). In this paper, we investigate the SLRs effect of the circular nano-array fabricated on the fiber tips theoretically. The difference between the 2D periodic and circular periodic arrays results in different resonant characteristics. For both structures, the resonant peaks due to the SLRs shift continuously as the array structure are adjusted. But for some specific arrangements, the circular nano-array may generate a single sharp resonant peak with extremely high enhancement, which originates from the collective coupling of the whole array. More interesting, the spatial pattern of the vector near-field corresponding to the sharp peak is independent of the polarization state of the incidence, facilitating its excitation and regulation. This finding may be helpful to design multifunctional all-fiber devices.