Cryptocurrency has recently attracted substantial interest from investors due to its underlying philosophy of decentralization and transparency. Considering cryptocurrency’s volatility and unique characteristics, accurate price prediction is essential for developing successful investment strategies. To this end, the authors of this work propose a novel framework that predicts the price of Bitcoin (BTC), a dominant cryptocurrency. For stable prediction performance in unseen price range, the change point detection technique is employed. In particular, it is used to segment time-series data so that normalization can be separately conducted based on segmentation. In addition, on-chain data, the unique records listed on the blockchain that are inherent in cryptocurrencies, are collected and utilized as input variables to predict prices. Furthermore, this work proposes self-attention-based multiple long short-term memory (SAM-LSTM), which consists of multiple LSTM modules for on-chain variable groups and the attention mechanism, for the prediction model. Experiments with real-world BTC price data and various method setups have proven the proposed framework’s effectiveness in BTC price prediction. The results are promising, with the highest MAE, RMSE, MSE, and MAPE values of 0.3462, 0.5035, 0.2536, and 1.3251, respectively.