Summary: In this paper, we study the \({L^2}\)-decay and the asymptotic stability of the weak solutions of the following three-dimensional Brinkman-Forchheimer equations in \({\mathbb{R}^3}\): \[{u_t} - \Delta u + au + b {|u|^\beta}u + \nabla p = 0.\] Firstly, we use the Fourier splitting method to study the decay of weak solutions in the \({L^2}\) space when \(\beta > \frac{7}{3}\). Then we investigate the asymptotic stability of the solutions to the system under large initial perturbation.