Hyperdimensional computing (HD) is an emerging paradigm for machine learning based on the evidence that the brain computes on highdimensional, distributed, representations of data. The main operation of HD is encoding, which transfers the input data to hyperspace by mapping each input feature to a hypervector, followed by a bundling procedure that adds up the hypervectors to realize the encoding hypervector. The operations of HD are simple and highly parallelizable, but the large number of operations hampers the efficiency of HD in embedded domain. In this paper, we propose SHEAR , an algorithmhardware co-optimization to improve the performance and energy consumption of HD computing. We gain insight from a prudent scheme of approximating the hypervectors that, thanks to error resiliency of HD, has minimal impact on accuracy while provides high prospect for hardware optimization. Unlike previous works that generate the encoding hypervectors in full precision and then and then perform ex-post quantization, we compute the encoding hypervectors in an approximate manner that saves resources yet affords high accuracy. We also propose a novel FPGA architecture that achieves striking performance through massive parallelism with low power consumption. Moreover, we develop a software framework that enables training HD models by emulating the proposed approximate encodings. The FPGA implementation of SHEAR achieves an average throughput boost of 104,904× (15.7×) and energy savings of up to 56,044× (301×) compared to state-of-the-art encoding methods implemented on Raspberry Pi 3 (GeForce GTX 1080 Ti) using practical machine learning datasets.