In the past decades, human activity recognition based on smart phones has played an important role in intelligent buildings, medical care and military fields. However, the CPU, storage space and computing power of smart phones are very limited, so the development of a lightweight human activity recognition learning model has become a research hotspot. In order to solve the above problems, this paper proposes a lightweight human activity recognition learning model (NCA-L2-SCNs) based on neighbourhood component analysis (NCA) and L2 regularized stochastic configuration networks (SCNs). First, Focusing on the problem of high dimensionality and poor separability of the human activity feature set, NCA is employed to select the high correlation feature subset from the feature set, thus enhancing the lightweight and recognition accuracy in the process of modeling computation. Second, aiming at the problem of overfitting when there are too many hidden layer nodes in SCNs, the L2 regularization method is adopted to enhance the generalization functionality of SCNs, in the meantime, the hidden layer parameters are generated by the supervision mechanism constraints, which greatly enhances the lightweight of SCNs models. Finally, the NCA-L2-SCNs model proposed in this paper is verified on the UCI HAR feature set. The experimental results show that compared with other state-of-the-art models, the lightweight model proposed in this paper, which is effective for human activity recognition, has better recognition accuracy and faster modeling speed.