Single-pixel imaging technology has a number of advantages over conventional imaging approaches, such as wide operation wavelength region, compressive sampling, low light radiation dose and insensitivity to distortion. Here, we report on a novel single-pixel imaging based on fractional Fourier transform (FRFT), which captures images by acquiring the fractional-domain information of targets. With the use of structured illumination of two-dimensional FRFT base patterns, FRFT coefficients of the object could be measured by single-pixel detection. Then, the object image is achieved by performing inverse FRFT on the measurements. Furthermore, the proposed method can reconstruct the object image from sub-Nyquist measurements because of the sparsity of image data in fractional domain. In comparison with traditional single-pixel imaging, it provides a new degree of freedom, namely fractional order, and therefore has more flexibility and new features for practical applications. In experiments, the proposed method has been applied for edge detection of object, with an adjustable parameter as a new degree of freedom.