This paper deals with two types of catadioptric telescope. The first type consists of an aspheric mirror and two thin aspheric correcting plates, which are located in front of the mirror and its focus respectively. The second type consists of a spherical mirror and an aspheric meniscus, which is an equivalent of a spherical Maksutov meniscus with a Schmidt thin aspheric plate. A series of excellent construction for these catadioptric telescopes have been obtained by optimization. Then great numbers of rays tracing results. The image qualities of these catadioptric telescopes are given in the tables and spot diagrams.