We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order k 1 on the mesh skeleton, together with cell-based polynomi-als that can be eliminated locally by static condensation. The HHO method leads to a primal formulation, supports polyhedral meshes with non-matching interfaces, is free of volumetric locking, the integration of the behavior law is performed only at cell-based quadrature nodes, and the tangent matrix in Newton's method is symmetric. Moreover, the principle of virtual work is satisfied locally with equilibrated tractions. Various two-and three-dimensional benchmarks are presented, as well as comparison against known solutions with an industrial software using conforming and mixed finite elements.