We introduce a framework that is capable of reconstructing mosaic from an image stream that contains parallax. As non-planar, non-distant scene is pictured under general camera motion, parallax is present in the image data. Constructing mosaic from such data is difficult because global parametric transformation that allows one image to be registered with another is lacking. In an earlier work one of us proposed to overcome the difficulty by the use of a third image. In this work we extend the three-image mosaicking mechanism for not three images but an image stream that contains parallax. We answer two questions: (1) how an image stream is divided into 3-image sets for the three-image mosaicking mechanism to iterate upon; and (2) how intermediate mosaic results over the various 3-image sets are accumulated to compose the overall mosaic at the most current image frame. Experimental results on real image data are also presented.