Accurate detection of ultra-low refractive indices (RIs) with high amplitude sensitivity (AS) is crucial for many applications, including effective environmental monitoring, bio-sensing, medical diagnostics, and the detection of harmful gases. For ultra-low RIs, the evanescent wave interacts weakly with the plasmonic layers, which makes it difficult to create sharp resonance peaks, resulting in reduced AS. To address this challenge, an efficient light-guiding mechanism with a carefully engineered cladding fiber design is necessary. In this paper, we propose a new type of anti-resonant solid core fiber (AR-SCF)-based surface plasmon resonance (SPR) sensor that simultaneously offers high AS and can detect ultra-low RIs in the near-infrared (NIR) wavelength regime. The proposed sensor architecture is relatively simple with six circular tubes in the cladding region. The light guidance relies on the anti-resonant guiding principle, which ensures better sensing performance and strong light confinement within the core region. The sensing and metallic layers are carefully deposited on the surfaces of the cladding and jacket tubes to enhance the sensing performance. Our comprehensive theoretical analysis demonstrates that the proposed sensor is capable of detecting ultra-low RIs ranging from 0.98 to 1.15, with an unprecedented AS of >5.5×103 RIU-1 near the RI of 1.0 and >3.2×103 RIU-1 at the RI of 1.10. In addition, the sensor shows a maximum wavelength sensitivity (WS) of 6000 nm/RIU for RI of 1.05 and a notable figure of merit (FOM) of 700 RIU-1. The proposed sensor could be a suitable candidate for on-chip RI sensing platforms because of its outstanding sensing performance.