We consider an i.i.d. supercritical bond percolation on Z^d , every edge is open with a probability p > p_c (d), where p_c (d) denotes the critical parameter for this percolation. We know that there exists almost surely a unique infinite open cluster C_p [7]. We are interested in the regularity properties in p of the anchored isoperimetric profile of the infinite cluster C_p. For d ≥ 2, we prove that the anchored isoperimetric profile defined in [4] is Lipschitz continuous on all intervals [p_0 , p_1 ] ⊂ (p_c (d), 1).