The input for stock market prediction is usually a period of stock price data with time series characteristics, which will keep changing over time and have more complex background relationships. How to effectively mine and fuse multiple heterogeneous data of the stock market is difficult to be handled by traditional recurrent neural networks (RNN). To solve this problem, we divide the regression model into an encoder and decoder structure. In this paper, we first use RNN technique for missing value complementation, then use the fusion model of bidirectional gate recurrent unit (BiGRU) and bidirectional long short-term memory network (BiLSTM) as the encoder to extract. Finally, the group method of data handling (GMDH) model is used as a decoder to obtain stock market prediction results based on the time series data features. A deep heuristic evolutionary regression model (BBGMDH) based on the fusion of BiGRU and BiLSTM is proposed by the above process. We have conducted extensive experiments on four real stock data, and the results show that BBGMDH significantly outperforms existing methods, verifying the effectiveness of the encoding-decoding stepwise regression model in stock price prediction tasks. The reason is that the encoding layer utilizes the powerful time series data processing technology of RNN to effectively extract the hidden features of stock data, and the decoding layer utilizes the GMDH heuristic evolutionary computation method to simulate the “genetic mutation selection evolution” process of an organism for the regression task of stock market prediction, making full use of their complementary properties. We provide a new solution to the regression prediction problem.