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In the present paper,we consider the nonlocal Kirchhoff problem -(ε2a +-εb ∫R3 |▽u|2)Δu +-u=Q(x)up,u ＞ 0 in R3,where a,b ＞ 0,1 ＜ p ＜ 5 and ε ＞ 0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.