The perpendicular-orbit circular scanning sensor， a new optical imaging system， can capture images with an ultra-wide swath width （thousand-kilometer level） and high resolution （meter level） that are much larger than those obtained by traditional satellites （with a single image being up to several hundred gigabytes）. A rigorous imaging model was constructed for the perpendicular-orbit circular scanning sensor based on an analysis of its imaging principles. Based on the characteristics of the perpendicular-orbit circular scanning sensor， a terrain-dependent control point layout scheme combined with DEM was developed. In addition， a method to determine the initial iteration interval was proposed using the coordinate of the sub-satellite point to solve the problem of back projection calculation failure under the condition of a wide swath， which could help obtain a solution from the object space coordinate to the image space coordinate within the whole scene range of an arbitrary-width image. In this study， a RFM construction test was conducted by simulating images with different swath width， orbital， and altitudinal data to explore the fitting accuracy of RFM in different object square coordinate systems. When the swath width of the image reaches 3 000 km， the RFM fit error is 3 004.25 and 1 939.04 pixels in different schemes. The RFM fit error constructed by the terrain-dependent scheme is 27.5 and 24.96 pixels when a geocentric rectangular coordinate system was used. Images captured by the perpendicular-orbit circular scanning sensor can have widths of several thousand kilometers； therefore， the accuracy of RPC is significantly affected by the curvature of earth， and the accuracy of RPC solved under the condition of geocentric rectangular coordinate system is better than that of a geodetic coordinate system. The initial exploration of the RFM accuracy of perpendicular-orbit circular scanning sensor images can provide a foundation for the application of the satellite.