Earth orbiting spacecrafts have become an integral part of our everyday lives. A real and growing concern for the safety and reliability of these satellites is the threat from collision with other orbiting objects including space debris. Size estimation of space object is an important task in evaluating its danger of a possible collision with operational spacecraft. RCS (Radar Cross Section) includes much information of space object, and extracting the feature of the object size from the RCS time series of narrowband radar is very helpful to radar target identification. Unfortunately, it is very difficult to get the information of target shape and size from its RCS. In this paper, based on the research of the characteristic of the ellipsoid's RCS, a shape estimation method of space object is proposed, and the problem of size estimation is studied further with a new method of size estimation proposed. The result using real radar data shows that this method is feasible to estimate the shape and two-dimensional sizes of the space object.