Remote sensing images (RSIs) encompass abundant spatial and spectral/temporal information, finding wide applications in various domains. However, during image acquisition and transmission, RSI often encounter noise interference, which adversely affects the accuracy of subsequent applications. To address this issue, this paper proposes a novel non-local fully connected tensor network (NLFCTN) decomposition algorithm for denoising RSI, aiming to fully exploit their global correlation and non-local self-similarity (NSS) characteristics. FCTN, as a recently developed tensor decomposition technique, exhibits remarkable capability in capturing global correlations and minimizing information loss. In addition, we introduce an efficient algorithm based on proximal alternating minimization (PAM) to efficiently solve the model and prove the convergence. The effectiveness of the proposed method is validated through denoising experiments on both simulated and real RSI data, employing objective evaluation metrics and subjective visual assessments. The results of the experiment show that the proposed method outperforms other RSI denoising techniques in terms of denoising performance.