Gaussian beam propagation through complicated optical systems is studied in detail by using matrix optics method. The results are generalized to the oases including (1) refractive indices of the object and image spaces are not the same (n1≠n2); (2) the transfer matrix elements of optical systems are complex or the element O is equal to zero. The effects of Gaissian limiting aperatore on the beam transmission are discussed. A comparison between the classical and Gaussian beam optics (n1≠n2,n1=n2) clearly illustrates their differences and relations.