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We construct Wong--Zakai approximations of time--inhomogeneous stochasticdifferential equations with regime switching (RSSDEs), and provide aconvergence rate. %Given a family of finite-variation processes$\{\mathcal{F}^{\lambda}\}_{\lambda\ge 0}$ that converge strongly to a standardBrownian motion $\mathcal{B}$, we construct pathwise approximations forregime-switching, time-inhomogeneous stochastic differential equations in theWong-Zakai sense. Moreover, we determine the rate of strong convergence to thesolutions of such regime-switching SDEs, showing that this rate is almost asgood as that of $\{\mathcal{F}^{\lambda}\}_{\lambda\ge 0}$ to $\mathcal{B}$. Inthe proposed approximations, the standard Brownian motion driving thetime-inhomogeneous RSSDEs is replaced by a family of finite--variationprocesses $\{\mathcal{F}^{\lambda}\}_{\lambda > 0}$. We show that if$\mathcal{F}^{\lambda}$ strongly converges to $\mathcal{B}$ at rate$\delta(\lambda)$, then the Wong--Zakai approximation strongly converges to theoriginal solution of the time--inhomogeneous RSSDE at rate $\delta(\lambda)\lambda^{\varepsilon}$, for any $\varepsilon > 0$. This is the first paper onWong--Zakai approximations for time--inhomogeneous RSSDEs, and significantlyextends the counterparts for time--homogeneous SDEs without regime switching inR\"{o}misch and Wakolbinger (1985).

Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching