L p-moment mixed quermassintegrals of convex bodies in R n are introduced. The Brunn-Minkowski type inequality and Aleksandrov-Fenchel type inequality are established for L p-moment mixed quermassintegrals that imply affine mixed quermassintegrals inequality, Lutwak's mixed polar projection inequality, and isoperimetric inequality for L p-moment mixed quermassintegrals. Inequalities of L p-moment mixed quermassintegrals of polar bodies are proved.