  A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which
there are no rainbow triangles. 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 $G=K_{3}$. Thus the
Gallai-Ramsey number $gr_{k}(K_{3}: K_{4}^{+})$ is obtained.
