  We derive criterion in the form of inequality based on quantum Fisher
information and quantum variance to detect multipartite entanglement. It can be
regarded as complementary of the well-established PPT criterion in the sense
that it can also detect bound entangled states. The inequality is motivated by
Y.Akbari-Kourbolagh $et\ al.$[Phys. Rev A. 99, 012304 (2019)] which introduced
a multipartite entanglement criterion based on quantum Fisher information. Our
criterion is experimentally measurable for detecting any $N$-qudit pure state
mixed with white noisy. We take several examples to illustrate that our
criterion has good performance for detecting certain entangled states.
