Abstract: Based on relative error covariarice matrix (RECM) information, a reduced-order model is proposed for solving linear inverse problem. The reduced-order model turns the high order model into an approximate lower order model, which can efficiently alleviate the computational load of the inversion algorithm. Thus, the computational complexity difficulty arose in the solution of linear inverse problem can be conquered, and this in turn promotes the implementation of the inversion algorithm. In addition, the reduced-order model can improve the estimate precision of those points that provide significant information to the reconstruction of the object.