For the benefit from accurate electricity price forecasting, not only can various electricity market stakeholders make proper decisions to gain profit in a competitive environment, but also power system stability can be improved. Nevertheless, because of the high volatility and uncertainty, it is an essential challenge to accurately forecast the electricity price. Considering that recurrent neural networks (RNNs) are suitable for processing time series data, in this paper, we propose a bidirectional long short-term memory (LSTM)-based forecasting model, BRIM, which splits the state neurons of a regular RNN into two parts: the forward states (using the historical electricity price information) are designed for processing the data in positive time direction and backward states (using the future price information available at inter-connected markets) for the data in negative time direction. Moreover, due to the fact that inter-connected power exchange markets show a common trend for other neighboring markets and can provide signaling information for each other, it is sensible to incorporate and exploit the impact of the neighboring markets on forecasting accuracy of electricity price. Specifically, future electricity prices of the interconnected market are utilized both as input features for forward LSTM and backward LSTM. By testing on day-ahead electricity prices in the European Power Exchange (EPEX), the experimental results show the superiority of the proposed method BRIM in enhancing predictive accuracy in comparison with the various benchmarks, and moreover Diebold-Mariano (DM) shows that the forecast accuracy of BRIM is not equal to other forecasting models, and thus indirectly demonstrates that BRIM statistically significantly outperforms other schemes.