This paper is concerned with the chemotaxis-Stokes system
equation(⋆)
under no-flux boundary conditions in a bounded domain Ω⊂R3 with smooth boundary. Here S is a matrix-valued sensitivity satisfying with some and α>0. We shall first establish the boundedness of (⋆) through a series of a priori estimate, and then propose the stabilization of the classical solution. This result gives a definite answer to the conjecture in Remark 1.2 by Y. Wang and X. Cao (2015) and extends the main result of that paper.