Groupwise image registration provides an unbiased registration solution upon a population of images, which can facilitate the subsequent population analysis. However, it is generally computationally expensive for performing groupwise registration on a large set of images. To alleviate this issue, we propose to utilize a fast initialization technique for speeding up the groupwise registration. Our main idea is to generate a set of simulated brain MRI samples with known deformations to their group center. This can be achieved in the training stage by two steps. First, a set of training brain MR images is registered to their group center with a certain existing groupwise registration method. Then, in order to augment the samples, we perform PCA on the set of obtained deformation fields (to the group center) to parameterize the deformation fields. In doing so, we can generate a large number of deformation fields, as well as their respective simulated samples using different parameters for PCA. In the application stage, when given a new set of testing brain MR images, we can mix them with the augmented training samples. Then, for each testing image, we can find its closest sample in the augmented training dataset for fast estimating its deformation field to the group center of the training set. In this way, a tentative group center of the testing image set can be immediately estimated, and the deformation field of each testing image to this estimated group center can be obtained. With this fast initialization for groupwise registration of testing images, we can finally use an existing groupwise registration method to quickly refine the groupwise registration results. Experimental results on ADNI dataset show the significantly improved computational efficiency and competitive registration accuracy, compared to state-of-the-art groupwise registration methods.