Semi-supervised learning is an important topic in machine learning. In this paper, a network-based semi-supervised classification method is proposed. Class labels are propagated by combined random-deterministic walking of particles and competition among them. Different from other graph-based methods, our model does not rely on loss function or regularizer. Computer simulations were performed with synthetic and real data, which show that the proposed method can classify arbitrarily distributed data, including linear non-separable data. Moreover, it is much faster due to lower order of complexity and it can achieve better results with few pre-labeled data than other graph based methods.