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Weyl semimetals [1-4] are extraordinary systems where exotic phenomena such as Fermi arcs [5, 6], pseudo-gauge fields [7-9] and quantum anomalies [10-12] arise from topological band degeneracy in crystalline solids for electrons and metamaterials for photons [13-18] and phonons [19-22]. On the other hand, higher-order topological insulators [23-26] unveil intriguing multidimensional topological physics beyond the conventional bulk-edge correspondences. However, it is unclear whether higher-order topology can emerge in Weyl semimetals. Here, we report the experimental discovery of higher-order Weyl semimetals in its phononic analog which exhibit topologicallyprotected boundary states in multiple dimensions. We create the physical realization of the higher-order Weyl semimetal in a chiral phononic crystal with uniaxial screw symmetry. Using near-field spectroscopies, we observe the chiral Fermi arcs on the surfaces and a new type of hinge arc states on the hinge boundaries. These topological boundary arc states link the projections of Weyl points in different dimensions and directions, and hence demonstrate higher-order multidimensional topological physics in Weyl semimetals. Our study establishes the fundamental connection between higher-