Long-range surface plasmon resonances (LRSPRs) are featured with longer propagation and deeper penetration, compared with conventional surface plasmon resonances (SPRs). Thus, LRSPR-based fiber sensors are considered to have great potential for highly sensitive detection in chemistry or biomedicine areas. Here, we propose and demonstrate a near-infrared LRSPR sensor based on a D-shaped honeycomb microstructured optical fiber (MOF) directly coated with gold film. Although there is no additional heterogeneous buffer layer, the optical field of the long-range surface plasmon polariton (LRSPP) mode penetrates strongly into the analyte region. Thus the effective refractive index of the LRSPP mode depends highly on the analyte's material refractive index and an abnormal dispersion relationship between the LRSPP mode and MOF's y-polarized core mode is observed. The mechanism of the LRSPR excitation in the coupling zone is attributed to an avoided crossing effect between these two modes. It also results in the generation of a narrow-bandwidth peak in the loss spectrum of the core mode. Further discussion shows that the resonance wavelength is mainly determined by the core size that is contributed by the MOF's cladding pitch, silica-web thickness and planar-layer-silica thickness together. It indicates that the operation wavelength of the proposed LRSPR device can be flexibly tuned in a broadband wavelength range, even longer than 2 µm, through appropriately designing the MOF's structural parameters. Finally, the proposed LRSPR sensor shows the highest wavelength sensitivity of 14700 nm/RIU and highest figure of merit of 475 RIU-1 for the analyte refractive index range from 1.33 to 1.39.