In this paper, we study the boundedness theory for Bergman projection in the operator-valued setting. More precisely, let D \mathbb {D} be the open unit disk in the complex plane C \mathbb {C} and M \mathcal {M} be a semifinite von Neumann algebra. We prove that ‖ P ( f ) ‖ L 1 , ∞ ( N ) ≤ C ‖ f ‖ L 1 ( N ) , \begin{equation*} \|P(f)\|_{L_{1,\infty }(\mathcal {N})}\leq C \|f\|_{L_1(\mathcal {N})}, \end{equation*} where N = L ∞ ( D ) ⊗ ¯ M \mathcal {N}=L_{\infty }(\mathbb {D})\bar {\otimes }\mathcal {M} and P P denotes the Bergman projection. Consequently, P P is bounded on L p ( N ) L_{p}(\mathcal {N}) with 1 > p > ∞ 1>p>\infty . As applications, we also obtain Kolmogorov and Zygmund inequalities for the Bergman projection P P .