With transaction data in the stock market, prediction methods based on neural network for the highest price of one stock in every daily trading day and per minute price of one stock in a daily trading day are explored in this paper. BP neural network and RBF neural network are used in the implementation of predictors. To normalize input/out data with stereographic projection method in prediction method base on BP neural network, stereographic projection and its' characteristic are discussed in this paper too. Experimental results show that the fluctuating prices of a stock can be predicted well with neural network based prediction method and neural network based prediction method is suitable to solve prediction task in stock market.