Suppose \(\mathfrak{B}(H)\) is the Banach algebra of all bounded linear operators on a Hilbert space \(H\) with \(\dim(H)\geq 3\). Let \(\gamma(.)\) denote the reduced minimum modulus of an operator. We charaterize surjective maps \(\varphi\) on \(\mathfrak{B}(H)\) satisfying \(\gamma(\varphi(T)\varphi(S))=\gamma(T S)\;\;\;(T, S\in \mathfrak{B}(H)).\) Also, we give the general form of surjective maps on \(\mathfrak B(H)\) preserving the reduced minimum modulus of Jordan triple products of operators.