We propose a point-by-point inscription method for fiber Bragg grating (FBG) fabrication using a femtosecond pulsed laser focused through a fiber polyimide coating, realizing a 2-μm-wavelength-band FBG. A femtosecond laser acts as the inscription laser, focused by a 63× oil lens. A first-order FBG was fabricated with a grating interval of 700 nm. The 15-μW pulsed laser was focused directly on the fiber core through the polyimide coating and cladding. A first-order FBG for 2004.8-nm light with more than 56% reflectances was fabricated. High wavelength sensitivity and linearity of the FBG were demonstrated by temperature and strain-sensing testing. The first-order FBG of 2004.8 and 2000.2 nm resonant wavelengths could be realized simultaneously through parallel inscription method in 3000 μm long grating area.