We report the discovery of ultra-diffuse galaxies (UDGs) in Abell 370 (A370; z=0.375). We find 46 UDGs in A370 from the images of the Hubble Frontier Fields. Most UDGs are low-luminosity red sequence galaxies, while a few of them are blue UDGs. We estimate the abundance of UDGs in A370, N(UDG)=644+/-104. Combining these results with those of Abell S1063 (z=0.348) and Abell 2744 (z=0.308), we derive a mean radial number density profile of UDGs in the three clusters. The number density profiles of UDGs and bright galaxies show a discrepancy in the central region of the clusters: the profile of UDGs shows a flattening as clustercentric distance decreases, while that of bright galaxies shows a continuous increase. This implies that UDGs are prone to disruption in the central region of the clusters. The relation between the abundance of UDGs and virial masses of their host systems is described by a power law with an index of nearly one: N(UDG){propto}M_200_^0.99+/-0.05^ for M_200_>10^13^M_{sun}_. We estimate approximately dynamical masses of UDGs using the fundamental manifold method and find that most UDGs have dwarf-like masses (M_200_<10^11^M_{sun}_). This implies that most UDGs have a dwarf-like origin and a small number of them could be failed L* galaxies. These results suggest that multiple origins may contribute to the formation and evolution of UDGs in massive galaxy clusters.