Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns, that are highly branched without any loop structure in clusters as those found in the experiment [Yamazaki and Mizuguchi: J. Phys. Soc. Jpn. 69 (2000) 2387]. Resulting patterns undergo the percolation transition upon changing the initial granular density, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.