By imposing suitable assumptions on the weighted function, (un- der the constraint of fixed weighted volume) we can prove a Brock-type isoperimetric inequality for Steklov-type eigenvalues of the Witten-Laplacian on bounded domains in a Euclidean space or a hyperbolic space. This con- clusion is actually an interesting extension of F. Brock’s classical result about the isoperimetric inequality for Steklov eigenvalues of the Laplacian given in the influential paper [Z. Angew. Math. Mech. 81 (2001) 69–71]. Besides, a related open problem has also been proposed. This talk is based on a joint-work with my student Shijie Zhang.