We present a new semi-discrete central scheme for approximating solutions of Hamilton-Jacobi equations on unstructured meshes. This scheme extends the numerical Hamiltonians of Kurganov et al. to unstructured grids. Similarly to the previous works on structured grids, a semi-discrete formulation of central schemes is made possible due to estimates of the local speeds of propagation. The consistency of the method is obtained following Abgrall's calculations for the consistency of an upwind Lax-Friedrichs scheme on unstructured grids. We conclude with comments on high-order reconstructions.