In this note, some operator inequalities for operator means and positive linear maps are investigated. The conclusion based on operator means is presented as follows: Let Φ : B(H) → B(K ) be a strictly positive unital linear map and h−11 IH ≤ A ≤ h1IH and h−12 IH ≤ B ≤ h2IH for positive real numbers h1, h2 ≥ 1. Then for p > 0 and an arbitrary operator mean σ, (Φ(A)σΦ(B))p ≤ αpΦp(Aσ∗B), where αp = max {( α2(h1 ,h2) 4 )p , 116α 2p(h1, h2) } , α(h1, h2) = (h1 + h−11 )σ(h2 + h −1