This paper considers the problem of modeling complex motions of pedestrians in a crowded environment. A number of methods have been proposed to predict the motion of a pedestrian or an object. However, it is still difficult to make a good prediction due to challenges, such as the complexity of pedestrian motions and outliers in a training set. This paper addresses these issues by proposing a robust autoregressive motion model based on Gaussian process regression using l1-norm based low-rank kernel matrix approximation, called PCGP-l1. The proposed method approximates a kernel matrix assuming that the kernel matrix can be well represented using a small number of dominating principal components, eliminating erroneous data. The proposed motion model is robust against outliers present in a training set and can reliably predict the motion of a pedestrian, such that it can be used by a robot for safe navigation in a crowded environment. The proposed method is applied to a number of regression and motion prediction problems to demonstrate its robustness and efficiency. The experimental results show that the proposed method considerably improves the motion prediction rate compared to other Gaussian process regression methods.