We study the dust surface potential for the complex dusty plasma with negative ions and with a three-parameter non-Maxwell velocity distribution. The plasma contains electrons, positive ions, negative ions, and negatively charged dust particles. By using the current equilibrium condition, we derive the relationship between the normalized dust surface potential and the dusty plasma parameters such as the normalized dust number density, the temperature ratio of negative ions to electrons, the density ratio of negative ions to positive ions, and the charge number of negative ions. The numerical analyses show that the relationship depends evidently on the three parameters in the non-Maxwell distribution when the dust surface potential is relatively smaller, but with increase of the potential, such dependence will weaken soon. The dust surface potential is negative and increases monotonously with increase of the dust density, and for the complex dusty plasma with the three-parameter non-Maxwell distribution, it is generally greater than that in the same plasma with the kappa-distribution and the Maxwellian distribution.
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