In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component \(X^{\varepsilon }\) is the solution of a stochastic differential equation with additional homogenization term, while the fast component \(\alpha ^{\varepsilon }\) is a switching process. We first prove the weak convergence of \(\{X^\varepsilon \}_{0<\varepsilon \leqslant 1}\) to \(\bar{X}\) in the space of continuous functions, as \(\varepsilon \rightarrow 0\) . Using the martingale problem approach and Poisson equation associated with a Markov chain, we identify this weak limiting process as the unique solution \(\bar{X}\) of a new stochastic differential equation, which has new drift and diffusion terms that differ from those in the original equation. Next, we prove the order 1/2 of weak convergence of \(X^{\varepsilon }_t\) to \(\bar{X}_t\) by applying suitable test functions \(\phi \) , for any \(t\in [0, T]\) . Additionally, we provide an example to illustrate that the order we achieve is optimal.
