  Genuine multipartite entanglement (GME) offers more significant advantages in
quantum information compared with entanglement. We propose a sufficient
criterion for the detection of GME based on local sum uncertainty relations for
chosen observables of subsystems. We apply the criterion to detect the GME
properties of noisy $n$-partite W state when $n = 3, 4, 5$ and $6$, and find
that the criterion can detect more noisy W states when $n$ ranges from 4 to 6.
Moreover, the criterion is also used to detect the genuine entanglement of
$3$-qutrit state. The result is stronger than that based on GME concurrence and
fisher information.
