Abstract: Minimization of 1-norm has been widely used to recover compressed sensing signal.However, it has no always close-form solution theoretically.This paper presents a fast recovery method of compressed sensing signal.In order to avoid solving the NP problems and the insolvable problems, a new objective function is designed to fit 0-norm of the signal and a new search direction is proposed to find the solution, with a solution speed equal to the speed of linear optimization.Experimental results show that the above method, with high compression ratio and good restoration effect, is well-suited for processing large data.