Properties of three smooth approximating functions for absolute value function are studied, and approximation degree is shown by images. Then a method for convex quadratic programming is proposed. After transforming convex quadratic programming into nonsmooth nonlinear equation system, and smoothing by smoothing approximation function, thus weSobtain smooth nonlinear equations, which can be solved by highSorderSNewton"sSmethod. Numerical results show that the method has fast convergence and fewer iterations.