Abstract: By using the general diffraction integration method,the transformation property of Bessel-Gaussian(BG) beam in a fractional Fourier plane was studied,and closed-form transformation expression was derived for the BG beam through the LohmannⅡ optical system.By using the derived formula,typical numerical calculation results were obtained to study the influences of the fractional order on the properties of BG beam in the fractional Fourier plane.It is shown that the intensity of BG beam depends on the fractional order p and the variation of the intensity with fractional order p is periodic.