High reliable decision-making results for black-start are required in smart grid. Based on the idea of entropy， a new method for the reliability analysis on the black-start decision-making results is proposed， and an index for quantifying the reliability level of black-start decision-making and measuring the decision-making level of the experts concerned is presented. The decision-making reliability level of each decision-maker such as dispatchers and/or other power system experts could be obtained by calculating the decision-making entropy， and then an integrated decision-making reliability level is attained. Based on the results of the reliability analysis， the decision-makers could reappraise their black-start strategies. As a result， the integrated reliability level could then be improved and the black-start decision-making results optimized. Furthermore， the reliability analysis could extend the theoretical framework of the black-start decision support system in smart grids， and its results would be helpful for dispatchers to understand the reliability of the obtained black-started restoration strategy and to ultimately make the optimal decision-making of the black-start strategy with the accepted reliability level. Numerical examples are served for demonstrating the developed method.