Fast structured illumination microscopy plays an important role in micro-nano detection due to the characteristics of high accuracy, high efficiency and strong adaptability. Traditional methods utilizes the linear region of the axial modulation response curve to achieve 3D topography recovery by building the relationship between the modulation and the actual height. However, the application of traditional methods is limited to its narrow dynamic measurement range since the linear region of axial modulation response curve is very short. In order to overcome the disadvantage, a double-differential fast structured illumination microscopy is proposed. By introducing two additional detection branches for building the double-differential axial modulation response curve to obtain a wider linear region, the proposed method can obtain a larger dynamic measurement range. Under the condition of a microscope objective with a numerical aperture of 0.9 and a magnification of 100, the dynamic measurement range is expanded from 380 nm to 760 nm in simulation and from 300 nm to 600 nm in actual experiment. The simulations and experimental results verify that the dynamic measurement range of double-differential fast structured illumination microscopy is twice as large as that of the traditional method under the same system parameters, which effectively broadens the application range of fast structured illumination microscopy.