  In this paper, by using of the definition Berezin symbol, we show some
Berezin number inequalities. Among other inequalities, it is shown that if $A,
B, X\in{\mathbb{B}}(\mathscr H)$, then $$\mathbf{ber}(AX\pm XA)\leqslant
\mathbf{ber}^{\frac{1}{2}}\left(A^*A+AA^*\right)\mathbf{ber}^{\frac{1}{2}}\left(X^*X+XX^*\right)$$
and
$$\mathbf{ber}^2(A^*XB)\leqslant\|X\|^2\mathbf{ber}(A^*A)\mathbf{ber}(B^*B).$$
