This work aims to elaborate a governance composite index for research laboratories in public university. This index is composed by an indicator of responsible liberalism associating effectiveness and ethics, to which are added an organizational management indicator and a strategic management indicator. To achieve the above aim, several methods are used, such as adjusted data envelopment analysis and geometric mean to aggregate indicators to calculate the composite index, Vigier index to compute responsible liberalism indicator, and tools to measure the validity and the reliability of indicators. The findings show that the developed index can be applied in any context.