A retrieval algorithm is proposed to retrieve tropospheric carbon monoxide (CO) profiles and total column from the Measurements Of Pollution In The Troposphere (MOPITT) radiances. A criteria to choose a background error covariance matrix, which represents a priori knowledge of vertical CO profiles, is derived to find a proper weight between measurements and background information. The proper chosen a priori error covariance matrix can be expected to constraint the retrieval results, to cut off the instrument errors and forward model errors from measurement information, to stabilize the matrix inversion and find reasonably good CO vertical profiles and total column amount. MOPITT CO retrieval results by using this method are compared with in-situ aircraft CO measurements from several MOPITT surface validation sites over Alaska, Massachusetts, Colorado and Hawaii. The CO profiles retrieved from this method are also compared to CO profiles retrieved from the Maximum Likelihood (fixed a priori matrix) method.