  Based on first principle calculations, we show that a family of nonmagnetic
materials including TaAs, TaP, NbAs and NbP are Weyl semimetal (WSM) without
inversion center. We find twelve pairs of Weyl points in the whole Brillouin
zone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), band
inversions in mirror invariant planes lead to gapless nodal rings in the
energy-momentum dispersion. The strong SOC in these materials then opens full
gaps in the mirror planes, generating nonzero mirror Chern numbers and Weyl
points off the mirror planes. The resulting surface state Fermi arc structures
on both (001) and (100) surfaces are also obtained and show interesting shapes,
pointing to fascinating playgrounds for future experimental studies.
