We propose and demonstrate a distributed surface plasmon resonance (SPR) fiber sensor based on a novel, simple, and effective incident angle adjusting method. For normal fiber SPR sensors, it is hard to realize distributed sensing because it is hard to produce two dynamic ranges (resonance wavebands) with a great difference. The dynamic range depends on the incident angle, and therefore, we propose an incident angle adjusting method that is implemented by grinding an eccentric-core fiber to different angles, which helps to produce different SPR wavebands with great difference, thus realizing distributed sensing. In our two cascaded distributed configuration, with the refractive index range of 1.333-1.385, the fiber grind angles are 9° and 17°, the testing wavelength ranges are 613-760 nm and 745-944 nm, and the average testing sensitivities are 2826 nm/RIU and 4738 nm/RIU, respectively. Larger resonance wavelengths are associated with larger testing sensitivities. This distributed fiber sensor has important significance in the fields of multichannel liquid refractive indices and temperature self-reference measurements.