Let φ be an analytic self-map on D, n ∈ N and ∈ H(D). We consider the essential norm of the generalized integral-type operator C n φ, : Q K p, q → Z µ that is defined as follows C n φ, f (z) = z 0 f (n) (φ(ξ))(ξ) dξ, for all f ∈ Q K p, q. We give an estimate for the essential norm of the above operator.