Multilayer graphene, with wide absorption spectrum and unique photoelectric properties, is an ideal material to make the next generation of photoelectric detector. Taking graphene interband tunneling theory as the foundation, a photoelectric detector model with the structure of multilayer graphene nanoribbons was proposed. Nanoribbons which contacted with source and drain electrode at the end were sandwiched between the semiconductor substrate and the top and back gate. Using this model, a photoelectric conversion mechanism of multilayer graphene nanoribbon detector was established. It discussed the working principle of the detector at different top gate voltage, studied the relationship between the source-drain current and the incident light energy, researched the influence of the bias voltage, the length of depletion and the values of band gap on the dark current, and analyzed the change of detector responsibility and detectivity with the incident light energy under the different parameters. The results show that, the responsibility of detector increases with the layers of nanoribbons, and are affected by the band gap, the length of depletion and the bias voltage. The maximum responsibility up to 103 A·W-1; By limiting on the top gate voltage, the band gap and other variables can control the dark current of system and increase the detectivity, the detectivity up to a maximum value of 109 cm Hz1/2·W-1. The structure of multilayer graphene nanoribbons can enhance the absorption of the incident light, improve the sensitivity of the detector and the detection capability of weak light, and realize the detection from THz to far infrared wavelength of incident light. The detection performance is far better than that of many quantum structures and narrow-band semiconductor structure of photoelectric detector.