We propose a novel approach for predicting on-going action with the assistance of a low-cost depth camera. Our approach introduces a soft regression-based early prediction framework. In this framework, we estimate soft labels for the subsequences at different progress levels, jointly learned with an action predictor. Our formulation of soft regression framework 1) overcomes a usual assumption in existing early action prediction systems that the progress level of on-going sequence is given in the testing stage; and 2) presents a theoretical framework to better resolve the ambiguity and uncertainty of subsequences at early performing stage. The proposed soft regression framework is further enhanced in order to take the relationships among subsequences and the discrepancy of soft labels over different classes into consideration, so that a Multiple Soft labels Recurrent Neural Network (MSRNN) is finally developed. For real-time performance, we also introduce a new RGB-D feature called "local accumulative frame feature (LAFF)", which can be computed efficiently by constructing an integral feature map. Our experiments on three RGB-D benchmark datasets and an unconstrained RGB action set demonstrate that the proposed regression-based early action prediction model outperforms existing models significantly and also show that the early action prediction on RGB-D sequence is more accurate than that on RGB channel.