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Let H be the Hermite operator -\Delta +|x|^2 on \mathbb{R}^n. We prove aweighted L^2 estimate of the maximal commutator operator \sup_{R>0}|[b,S_R^\lambda(H)](f)|, where [b, S_R^\lambda(H)](f) = bS_R^\lambda(H) f -S_R^\lambda(H)(bf) is the commutator of a BMO function b and the Bochner-Rieszmeans S_R^\lambda(H) for the Hermite operator H. As an application, we obtainthe almost everywhere convergence of [b, S_R^\lambda(H)](f) for large \lambdaand f\in L^p(\mathbb{R}^n).

A weighted L^2 estimate of Commutators of Bochner-Riesz Operators for Hermite operator