Generative broad Bayesian (GBB) imputer, a novel nonparametric data-driven tool for missing data imputation with uncertainty quantification, is proposed. The proposed imputer aims to generate missing data in an iterative manner based on an augmentable broad Bayesian learning network. The procedure consists of the preparatory and tuning phase. The preparatory phase provides preliminary imputation of the missing data to develop a complete dataset. The tuning phase refines the accuracy of the imputation results based on the augmented learning network. There are three appealing features of the proposed GBB imputer: (i) the nonparametric generative scheme provides a universal tool for missing data imputation without constraints on the type of data attribution, missing data pattern, or requirement of the prior information about the dataset; (ii) the quantified uncertainty of the imputation results reflects the associated reliability and provides a rational termination indicator for the iterative imputation procedure; and (iii) the learning network can be augmented progressively to adopt architectural reconfigurations based on the inherited information of the trained network for efficient imputation. To demonstrate the efficacy and applicability of the proposed GBB imputer, we present two simulated examples under various scenarios and a case study with the achieved in-situ seismic records of the 2016 M6.5 Norcia earthquake.