In this paper, we propose a robust incremental principal component analysis (IPCA) for stream data that can handle missing values on an ongoing basis. In the proposed IPCA, a missing value is substituted with the value estimated from a conditional probability density function. The conditional probability density functions are incrementally updated when new data are given. In the experiments, we evaluate the performance for both artificial and real data sets through the comparison with the two conventional approaches to handing missing values. We first investigate the estimation errors of missing values. The experimental results demonstrate that the proposed IPCA gives lower estimation errors compared to the other approaches. Next, we investigate the approximation accuracy of eigenvectors. The results show that the proposed IPCA has relatively good accuracy of eigenvectors not only for major components but also for minor components.