A kind of uniform density and thickness isosceles triangle cantilever beam is designed to realize linear tuning of Bragg wavelength of fiber grating without chirping by adjusting the deflection of the free end that is the vertex part of the triangle. The tuning is demonstrated experimentally within the range of 4.5 nm. After introducing a correction index η=0.71, experimental results agree with the theoretical value. The form of the reflected spectrum is related to the quality of pasting between fiber Bragg grating and the beam.