Support vector machine (SVM) is an efficient classifier for electroencephalogram (EEG) based gesture recognition whose applications usually require low hardware cost and low processing latency. Even though the training process can be unloaded to offline computing, the real-time classification process still suffers from large computing complexity, making it difficult to implement on wearable devices. Stochastic computing is a promising low hardware cost and low power consumption implementation candidate. In this paper, a novel stochastic computing based SVM classifier is proposed for EEG based gesture recognition to reduce the hardware cost. Besides, to overcome the long latency drawback of stochastic computing, a parallelism optimization method is utilized in the proposed design. According to the evaluation results, the proposed stochastic SVM classifier significantly outperforms the existing binary schemes on hardware cost and achieve comparable classification accuracy with float-point performance.