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In today’s world, Free Space Optical (FSO) communication under atmospheric turbulence continues to be an active area of research and development across various applications. Through the application of advanced techniques and technologies, FSO systems strive to achieve reliable, high-capacity data transmission in challenging atmospheric conditions. Due to the specific characteristics of gamma-gamma turbulence, it poses signal fading, scintillation, and link failures caused by turbulence can lead to service interruptions and impact the overall connectivity and network performance. However, it requires careful consideration of the environmental conditions and the use of appropriate techniques to ensure reliable and high-quality data transmission. Hence, there is a need to develop a low-complexity parameter estimation using an improved deep learning technique with low Bit Error Rate (BER) and low Mean Square Error (MSE). This paper propose a Hierarchical Attention-Echo State Network (HA-ES Net) model to estimate the parameters over gamma-gamma turbulence channels in FSO communications. HA-ES Net model leverages deep learning, attention mechanisms, and the ESN architecture. In this, the attention mechanism allows the network to selectively attend to informative channel characteristics and suppress noise and irrelevant information. Echo state property helps in learning and capturing the underlying dynamics of the FSO channel, enabling robust estimation even in the presence of noise and interference. Hence the hierarchical structure of HA-ES Net enables the network to learn and model the FSO channel in a more efficient manner. This reduces the complexity of training the network compared to other traditional approaches, making it feasible to implement HA-ES Net for FSO channel estimation. The simulation outcomes illustrate that the HA-ES Net model achieves strong estimation performance, characterized by low BER, low MSE, and minimal computational complexity.