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A kind of time-dependent mixed stochastic differential equations driven by Brownian motions and fractional Brownian motions with Hurst parameter $H>\frac{1}{2}$ is considered. We prove that the rate of convergence of Euler approximation of the solutions can be estimated by $O(\delta^{\frac{1}{2}\wedge(2H-1)})$ in probability, where $\delta$ is the diameter of the partition used for discretization.