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For two given graphs $H, G$ and two positive integers $k,s$ with that $s\\leq k$, the $k$-colored Gallai-Ramsey number $gr_{k}(K_{3}: s\\cdot H,~ (k-s)\\cdot G)$ is the minimum integer $n$ such that every Gallai $k$-colored $K_{n}$ contains a monochromatic copy of $H$ colored by one of the first $s$ colors or a monochromatic copy of $G$ colored by one of the remaining $k-s$ colors. In this paper, we determine the value of Gallai-Ramsey number in the case that $H=K_{4}^{+}$ and $G=K_{3}$. 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