In this paper, we obtain some Berezin number inequalities based on the definition of Berezin symbol. Among other inequalities, we show that if A, B be positive definite operators in B(H), and AB is the geometric mean of them, then ber 2 (AB) ≤ ber A 2 + B 2 2 − 1 2 inf λ∈Ω ζ(ˆ k λ), where ζ(ˆ k λ) = (A − B) ˆ k λ , ˆ k λ 2 , andˆkandˆ andˆk λ is the normalized reproducing kernel of the space H for λ belong to some set Ω,