The ion sheath instability with half the ion plasma frequency was observed around the separation grid in a double plasma containing negative ions, where the dominant negative ion species was specified from the dispersion relation of the ion acoustic wave. Detailed behavior of ion sheath instability was examined as a function of concentration of negative ions and bias potential of the separation grid. By measuring the sheath structure formed around the separation grid, it was found that when the negative ion density was increased, the ion sheath instability was suppressed. Furthermore, the peak frequency decreased with an increasing concentration of negative ions.