  We propose a leptoquark model simultaneously to explain anomalies of muon
anomalous magnetic dipole moment and $b\to s \mu\bar\mu$ in light of
experimental reports very recently. Here, we satisfy several stringent
constraints such as $\mu\to e\gamma$ and meson mixings. In addition, we find
these leptoquarks also play an role in generating tiny neutrino masses at
one-loop level without introducing any additional symmetries. We have numerical
analysis and show how degrees our parameter space is restricted.
