A temperature-insensitive acceleration sensor using two fibre Bragg gratings (FBGs), based on reflection spectrum intensity modulation and optical power detection, is proposed and demonstrated. A cantilever beam is used to generate acceleration-induced axial strain along two sensing gratings, which are glued on the two opposite surfaces of the beam. Because the two gratings operate within the linear spectral range of a light source, formed by a thermally-tunable extrinsic Fabry--Perot optical filter, the intensity difference of the two reflections from the gratings is proportional to the acceleration applied. This eliminates the need for sophisticated wavelength interrogation of the gratings, and it also endows the sensor with immunity to temperature variation. Compared with a commercial micromachined accelerometer, the sensor is proven to be capable of accurately detecting acceleration.