In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let $F$  be a family of meromorphic functions in the plane domain $D subseteq mathbb{C}$ and $n, k$ be two positive integers such that $n geq k +1$, and let $a, b$ be two finite complex constants such that $a
eq 0$. Suppose that (1) $f + a(f^{(k)})^n$ and $g + a(g^{(k)})^n$ share $b$ in $D$ for every pair of functions $f, g in F$; (2) All zeros of $f$ have multiplicity at least $k + 2$ and all poles of $f$ have multiplicity at least $2$ for each $f in F$ in $D$; (3) Zeros of
$f^{(k)}(z)$ are not the $b$ points of $f(z)$ for each $f in F$ in $D$. Then $F$ is normal in $D$. And some examples are provided to show the result is sharp

Keywords: meromorphic functions, shared value, normal family