Summary: The advances of systems biology have raised a large number of mathematical models for exploring the dynamic property of biological systems. A challenging issue in mathematical modeling is how to study the influence of parameter variation on system property. Robustness and sensitivity are two major measurements to describe the dynamic property of a system against the variation of model parameters. For stochastic models of discrete chemical reaction systems, although these two properties have been studied separately, no work has been done so far to investigate these two properties together. In this work, we propose an integrated framework to study these two properties for a biological system simultaneously. We also consider a stochastic model with intrinsic noise for the Nanog gene network based on a published model that studies extrinsic noise only. For the stochastic model of Nanog gene network, we identify key coefficients that have more influence on the network dynamics than the others through sensitivity analysis. In addition, robustness analysis suggests that the model parameters can be classified into four types regarding the bistability property of Nanog expression levels. Numerical results suggest that the proposed framework is an efficient approach to study the sensitivity and robustness properties of biological network models.