Realistic action recognition has been one of the most challenging research topics in computer vision. The existing methods are commonly based on non-probabilistic classification, predicting category labels but not providing an estimation of uncertainty. In this paper, we propose a probabilistic framework using Gaussian processes (GPs), which can tackle regression problems with explicit uncertain models, for action recognition. A major challenge for GPs when applied to large-scale realistic data is that a large covariance matrix needs to be inverted during inference. Additionally, from the manifold perspective, the intrinsic structure of the data space is only constrained by a local neighborhood and data relationships with far-distance usually can be ignored. Thus, we design our GPs covariance matrix via the proposed ℓ1 construction and a local approximation (LA) covariance weight updating method, which are demonstrated to be robust to data noise, automatically sparse and adaptive to the neighborhood. Extensive experiments on four realistic datasets, i.e., UCF YouTube, UCF Sports, Hollywood2 and HMDB51, show the competitive results of ℓ1-GPs compared with state-of-the-art methods on action recognition tasks.