Abstract: Based on fractal characteristics of the fracture surface of concrete, a series of Weierstrass-Mandelbrot (W-M) fractal surfaces of concrete satisfying certain fractal conditions are built. The multi-fractal characteristics of the W-M fracture surface of concrete are studied to calculate the multi-fractal spectrum of fracture surface of concrete. Considering the geometrical properties of the multi-fractal spectrum of concrete, the method of minimum squares is applied to the quadratic fitting of multi-fractal spectrum of fracture surface. The fitted function is quantitatively analyzed to simplify the calculation of multi-fractal properties of concrete. Comparisons between test results and theoretical calculation results verify that the quadratic fitting method of multi-fractal spectrum fits the multi-fractal spectrum of fracture surface of concrete well, and the evolution rules and trend are forecasted accurately. The research results can be applied in further research about mechanism of fracture surface formation in concrete and the optimization design of concrete structure.