Method of moments (MOM) is a common numerical method for solving electromagnetics, which is used widely owing to its high accuracy. As the traditional MOM is applied to solving electromagnetic problem in both spatial and frequency domains, the matrix equation generated from the integral equation must be solved repeatedly since small spatial increments and frequency increments are both required. To resolve problems of this kind, the compressive sensing (CS) theory combined with the asymptotic waveform evaluation (AWE) is introduced to form a new efficient computational method. Firstly, a new incident source is constructed based on CS theory, in which much spatial information is included. Secondly, illuminated by the new incident source, the new equation is solved by AWE technique, and finally a fast implement is formed for solving electromagnetic scattering characteristics in both spatial and frequency domains.