In this paper we investigate the dust surface potential at the sheath edge of electronegative dusty plasmas theoretically, using the standard fluid model for the sheath and treating electrons and negative ions as Boltzmann particles but positive ions and dust grains as cold fluids.The dust charging model is self-consistently coupled with the sheath formation criterion by the dust surface potential and the ion Mach number, moreover the dust density variation is taken into account. The numerical results reveal that the dust number density and negative ion number density as well as its temperature can significantly affect the dust surface potential at the sheath edge.