Compressed Sensing (CS) is a new framework for simultaneous sensing and compression, and how to recover sparse signal form limited measurements is the key problem in CS. A fast and stable method, called Expectation Minimization of approximate norm (abr. EML0), is proposed for sparse signal reconstruction with noisy measurements. The basic idea of the method is that sparse signal is recovered by minimizing the expectation of approximate norm, and then the expectation model by statistical character of noise is simplified so that the expectation model can be solved by the steepest descent method. Simulation results show that the proposed method provides better accuracy than existing methods at lower computational cost.