The invention provides an outward-turning type coaxial cylinder viscometer of a hollow cylinder type optical fiber Bragg grating, comprising a torsion measurement grating, a temperature compensation grating, an elastic hollow cylinder, an L-shaped temperature compensator, a stator and a viscometer measuring system which is composed of a spectrum analyzer, an ASE light source, a coupler and an optical fiber; the inner wall of the elastic hollow cylinder is pasted with the torsion measurement grating and the L-shaped temperature compensator, a long side of the compensator is pasted with the temperature compensation grating. According to the measured value of torsion and temperature sensitivity difference of the torsion measurement grating and the temperature compensation grating, the compensation of torque measurement disturbed by temperature fluctuation is realized by adopting differential operation, so as to realize accurate measurement of the torque. One end of the optical fiber is respectively connected with the spectrum analyzer and the ASE light source by the coupler, the other end thereof is connected with the optical fiber Bragg grating; wideband laser emitted by the ASE light source enters into the optical fiber Bragg grating, viscosity number is directly read out by wavelength displacement operation through an embedded computer of the analyzer. The sensor is suitable for measuring the viscosity of various fluids.