First-principles calculations have recently been used to develop comprehensive databases of nonmagnetic topological materials that are protected by time-reversal or crystalline symmetry. However, owing to the low symmetry requirement of Weyl points, a symmetry-based approach to identifying topological states cannot be applied to Weyl semimetals (WSMs). To date, WSMs with Weyl points in arbitrary positions are absent from the well-known databases. In this work, we develop an efficient algorithm to search for Weyl points automatically and establish a database of nonmagnetic WSMs with Weyl points near the Fermi level based on the experimental non-centrosymmetric crystal structures in the Inorganic Crystal Structure Database (ICSD). In total, 46 Weyl semimetals were discovered to have nearly clean Fermi surfaces and Weyl points within 300 meV of the Fermi level. Nine of them are chiral structures which may exhibit the quantized circular photogalvanic effect. In addition, the nonlinear optical response is studied and the giant shift current is explored. Besides nonmagnetic WSMs, our powerful tools can also be used in the discovery of magnetic topological materials.