Computational imaging spectrometry (CIS) has drawn great attention in recent years. It has the advantages of high optical throughput, snapshot imaging and so on. On the other hand, CIS has the disadvantage of insufficiency in sparse sampling which reduce the accuracy of reconstructed spatial-spectral data. By analyzing the optical property of CIS, a continuous pushbroom computational imaging spectrometry (CPCIS) is presented. In CPCIS, the orthogonal cyclic coded aperture was used, and the continuous scanning line by line was implemented through platform moving. The entire spatial-spectral data was reconstructed by orthogonal inversion. According to the imaging simulation and experiment, the aliasing in spatial-spectral image was eliminated, and the reconstructed image was well satisfied. Comparing to multiframe CIS, CPCIS has no moveable element, which can image without staring the object, thus it is suitable for the airborne and spaceborne remote sensing applications.