Weyl semimetals (WSMs)1 exhibit phenomena such as Fermi arc surface states, pseudo-gauge fields and quantum anomalies that arise from topological band degeneracy in crystalline solids for electrons1 and metamaterials for photons2 and phonons3. Here we report a higher-order Weyl semimetal (HOWSM) in a phononic system that exhibits topologically protected boundary states in multiple dimensions. We created the physical realization of the HOWSM in a chiral phononic crystal with uniaxial screw symmetry. Using acoustic pump-probe spectroscopies, we observed coexisting chiral Fermi arc states on two-dimensional surfaces and dispersive hinge arc states on one-dimensional hinge boundaries. These topological boundary states link the projections of the Weyl points (WPs) in different dimensions and directions, and hence demonstrate the higher-order topological physics4-8 in WSMs. Our study further establishes the fundamental connection between higher-order topology and Weyl physics in crystalline materials and should stimulate further work on other potential materials, such as higher-order topological nodal-line semimetals.