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Aiming at the traditional Shannon-Nyquist sample theorem argued that under the guarantee of signal reconstruction accuracy, the sampling frequency should be two times more than the primitive signal sampling frequency, a sparse signal construction method based on compressed sensing and improved adaptive orthogonal matching was proposed. Firstly, the compressed sensing and signal construction function was set, then the classic orthogonal matching pursuit algorithm was summarized, and the atom re-selection method was designed, namely, by computing the QR decomposition of signal and energy selective set, and by computing the relation between remain value and atom to get the relative selective atom set, and the intersection between energy selective atom set and relative selective set was built as the final supporting atom set. Finally, the algorithm for signal construction was defined. The simulation experiment was operated in Matlab environment, and the result shows the method can realize sparse signal construction with less construction error, and compared with the other methods, it has the advantage of rapid convergence and good construction effect.