The biosignals consist of several sensors that collect time series information. Since time series contain temporal dependencies, they are difficult to process by existing machine learning algorithms. Hyper-Dimensional Computing (HDC) is introduced as a brain-inspired paradigm for lightweight time series classification. However, there are the following drawbacks with existing HDC algorithms: (1) low classification accuracy that comes from linear hyperdimensional representation, (2) lack of real-time learning support due to costly and non-hardware friendly operations, and (3) unable to build up a strong model from partially labeled data.In this paper, we propose TempHD, a novel hyperdimensional computing method for efficient and accurate biosignal classification. We first develop a novel non-linear hyperdimensional encoding that maps data points into high-dimensional space. Unlike existing HDC solutions that use costly mathematics for encoding, TempHD preserves spatial-temporal information of data in original space before mapping data into high-dimensional space. To obtain the most informative representation, our encoding method considers the non-linear interactions between both spatial sensors and temporally sampled data. Our evaluation shows that TempHD provides higher classification accuracy, significantly higher computation efficiency, and, more importantly, the capability to learn from partially labeled data. We evaluate TempHD effectiveness on noisy EEG data used for a brain-machine interface. Our results show that TempHD achieves, on average, 2.3% higher classification accuracy as well as 7.7× and 21.8× speedup for training and testing time compared to state-of-the-art HDC algorithms, respectively.