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Abstract In this paper, we introduce the L p $L_{p}$ -mixed mean zonoid of convex bodies K and L, and we prove some important properties for the L p $L_{p}$ -mixed mean zonoid, such as monotonicity, GL ( n ) $\operatorname{GL}(n)$ covariance, and so on. We also establish new affine isoperimetric inequalities for the L p $L_{p}$ -mixed mean zonoid.