With maleic anhydride grafted polypropylene (PP-g-MAH) as a compatibilizer, composites of block-copolymerized polypropylene (B-PP)/nanoclay were prepared. The effects of the PP-g-MAH and nanoclay content on the crystallization and rheological properties of B-PP were investigated. The microcellular foaming behavior of the B-PP/nanoclay composite material was studied with a single-screw extruder foaming system with supercritical (SC) carbon dioxide (CO 2 ) as the foaming agent. The experimental results show that the addition of nanoclay and PP-g-MAH decreased the melt strength and complex viscosity of B-PP. When 3 wt % SC CO 2 was injected as the foaming agent for the extrusion foaming process, the introduction of nanoclay and PP-g-MAH significantly increased the expansion ratio of the obtained foamed samples as compared with that of the pure B-PP matrix, lowered the die pressure, and increased the cell population density of the foamed samples to some extent. V C 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44094.