Gaussian process regression (GPR) has shown superiority in terms of state estimation for its nonparametric characteristic and uncertainty prediction ability. Due to its heavy computational complexity, GPR is generally used for small datasets. To efficiently deal with the big data, the sparse spectrum approximation method has been successfully applied to GPR to decrease the computational complexity. However, the stationarity of this method is a strict assumption for data and usually mismatches the industrial processes. In this article, we proposed a sparse nonstationary GPR, which can deal with the nonstationary relationship among samples and make the model more flexible, to settle the aforementioned problems. Furthermore, the performance of the proposed method is evaluated using three public datasets and a sampled diesel engine dataset, and the results show the superiority of our proposed method in terms of accuracy.