Let ϕ be an analytic self-map of the unit disk D and u ∈ H(D), the space of analytic functions on D. The weighted composition operator, denoted by uC ϕ , is defined byIn this paper, we give three different estimates for the essential norm of the operator uC ϕ from H ∞ into the Zygmund space, denoted by Z. In particular, we show that uC ϕ e,H ∞ →Z ≈ lim sup n→∞ uϕ n Z .