In this paper, we study the weighted estimates for multilinear
Calder\'{o}n-Zygmund operators %with multiple APβ weights from
Lp1β(w1β)Γ...ΓLpmβ(wmβ) to Lp(vwβ), where 1<p,p1β,...,pmβ<β with 1/p1β+...+1/pmβ=1/p and w=(w1β,...,wmβ)
is a multiple APβ weight. We give weak and strong type weighted
estimates of mixed Apβ-Aββ type. Moreover, the strong type weighted
estimate is sharp whenever maxiβpiββ€pβ²/(mpβ1)