We report ground state energies and structural properties for small helium clusters (He-4) containing a H- impurity computed by means of variational and diffusion Monte Carlo methods. Except for (He2H-)-He-4 that has a noticeable contribution from collinear geometries where the H- impurity lies between the two He-4 atoms, our results show that (HeNH-)-He-4 clusters have a compact He-4(N) subsystem that binds the H- impurity on its surface. The results for N greater than or equal to 3 can be interpreted invoking the different features of the minima of the He-He and He-H- interaction potentials.