Dirac-Weyl semimetal is a novel type of topological phase that features the coexistence of Dirac and Weyl points in momentum space. In this study, a photonic Dirac-Weyl semimetal is proposed by introducing screw rotation symmetries into a spatial inversion symmetry-lacking system. A realistic metacrystal structure is designed for experimental consideration. The screw rotation symmetries are crucial for the existence of Dirac points, whose Z2 topology is revealed by the (010) surface states. Meanwhile, two pairs of ideal Weyl points at the same frequency are protected by D2d point group symmetries. The Dirac points and Weyl points reside in a clean frequency interval. The proposed photonic Dirac-Weyl semimetal provides a versatile platform for exploring the interaction between Dirac and Weyl semimetals and exploiting possible photonic topological devices.