In the paper, we have demonstrated an azobenzene-coated fiber Bragg grating (FBG) for monitoring ultraviolet light (UV) intensity in remote measurement. The elasticity of the coated azobenzene polymer is changed by the UV light, which induces a center wavelength change corresponding to the change of the FBG's grating period. The wavelength shift resulting from both UV light and other light with the wavelength out of the UV range was about 0.18 nm. In order to improve the accuracy of the measurement, the center wavelength shift caused by radiant heat of the light source was sufficiently removed by using a thermal filter. The amount of the center wavelength shift was consequently reduced to 0.06 nm, compared to the result without the thermal filter. Also, the FBGs coated by using azobenzene polymer were produced by two different methods; thermal casting and UV curing. Considering temperature dependence, UV curing is more suitable than thermal casting in UV sensor application of the azobenzene-coated FBG. In addition, we have confirmed the wavelength dependence of the optical sensor by means of four different band pass filters. Thus, we found out that the center wavelength shift per unit intensity is 0.029 [arb. unit] as a maximum value at 370 nm wavelength region and that the absorption spectrum of the azobenzene polymer was very consistent with the wavelength dependence of the azobenzene-coated FBG.