We experimentally demonstrated the fabrication of fiber Bragg gratings by using femtosecond laser point-by-point inscription. It is easy to create fiber Bragg gratings with different grating periods by changing the translation speed of the optical fiber. Firstly, laser pulse energy was optimized to improve the transmission spectra of fiber Bragg gratings. Then, a fiber Bragg grating was inscribed in a side-polished fiber to work as a refractive index sensor based on the evanescent field. There is a nonlinear relationship between Bragg wavelength and surrounding refractive index, where a refractive index sensitivity of ~30 nm/RIU has been achieved at 1.450. Thus, such side-polished FBGs could be used to develop a promising biochemical sensor.