This paper proposes the application of bagging to obtain more robust and accurate predictions using Gaussian process regression models. The training data are re-sampled using the bootstrap method to form several training sets, from which multiple Gaussian process models are developed and combined through weighting to provide predictions. A number of weighting methods for model combination are discussed, including the simple averaging and the weighted averaging rules. We propose to weight the models by the inverse of their predictive variance, and thus the prediction uncertainty of the models is automatically accounted for. The bagging method for Gaussian process regression is successfully applied to the inferential estimation of quality variables in an industrial chemical plant.