Accurate estimation of forest canopy height is crucial for biomass inversion, carbon storage assessment, and forestry management. However, deep learning methods are underutilized compared to machine learning. This paper introduces the convolutional neural network–bidirectional long short-term memory (CNN-BiLSTM) model and proposes a Convolutional Neural network–spatial channel attention–bidirectional long short-term memory (CNN-SCA-BiLSTM) model, incorporating dual attention mechanisms for richer feature extraction. A dataset comprising vegetation indices and canopy height data from forest regions in Luoyang, specifically within the 8–20 m range, is used for a comparative analysis of multiple models, with accuracy evaluated based on the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). The results demonstrate that (1) the CNN-BiLSTM model exhibits strong potential (MAE = 1.6554 m, RMSE = 2.2393 m, R² = 0.9115) and (2) the CNN-SCA-BiLSTM model, while slightly less efficient (<1%), demonstrates improved performance. It reduces the MAE by 0.3047 m, the RMSE by 0.6420 m, and increases the R² value by 0.0495. Furthermore, the model is utilized to generate a canopy height map (MAE = 5.2332 m, RMSE = 7.0426 m) for Henan in the Yellow River Basin for the year 2022. The canopy height is primarily distributed around 5–20 m, approaching the accuracy levels of global maps (MAE = 4.0 m, RMSE = 6.0 m).