The field of view (FOV) of pushbroom hyperspectral imager is limited by the compromise of the detector scale and requirements of spatial resolution. Combining imagers along the sampling direction effectively expands its FOV and improves the imaging efficiency. Due to the small overlapping area between the adjacent imagers, stitching the images using traditional methods need a large amount of ground control points (GCPs) or additional strips, which reduce the efficiency of both image acquisition and processing. This paper proposed a new method to precisely stitch images acquired from multiple pushbroom imagers. First, the relative orientation model was built based on the homonymy points to calculate the relative relationship between the adjacent imagers. Then rigorous geometric imaging model was adopted to generate a seamless stitching image. Simulation data was used to verify the accuracy of the method and to quantitatively analyze the effect of different error sources. Results show that the stitching accuracy is better than two pixels. Overall, this method provides a novel solution for stitching airborne multiple pushbroom images, to generate the seamless stitching image with wide FOV.