<p>In this paper we discuss the approximation of the spectrum of the Steklov eigenvalue problem, by using the well known Hybrid High-Order (HHO) method. The analysis developed in this work is partially based on the existing literature about the HHO method for the Laplacian eigenvalue problem. As usual with HHO methods, we are able to eliminate the volume unknowns, by introducing a suitable discrete solver operator. This allows us to numerically solve on the skeleton of the mesh, reducing the computational cost. The a priori error analysis lets us to prove optimal convergence rates for the eigenvalues and the eigenfunctions, when the latter are smooth enough. Numerical examples that confirm our theoretical findings are provided.</p>