This article introduces Gaussian process regression and shows its application with time-course microarray gene expression data. Gene screening for yeast cell cycle microarray expression data is accomplished with a ratio of log marginal likelihood that uses Gaussian process regression with a squared exponential covariance kernel function. Gaussian process regression fitting with each gene is done and shown with the nine top ranking genes. With the screened data the Gaussian model-based clustering is done and its silhouette values are calculated for cluster validity.