Few-shot learning (FSL) uses prior knowledge and supervised experience to effectively classify hyperspectral images (HSIs), thereby reducing the cost of large numbers of labeled samples. However, existing few-shot methods ignore the correlation between cross-domain feature channels, and the feature representation ability is insufficient. To address above issue, this paper proposes a novel Residual Channel Attention Based Sample Adaptation Few-Shot Learning for Hyperspectral Image Classification(RCASA-FSL) for hyperspectral image classification (HSIC), which can capture and enhance cross-domain dependencies through multi-layer residual connection and random-based feature recalibration. Specifically, a Deep Residual Feature Channel Attention Mechanism (DRFCAM) is designed to obtain cross-domain dependencies by residual concatenation, and further the residual structure is stacked for mining depth discrimination information. Furthermore, a new Random-based Feature Recalibration Module (RFRM) is proposed to reassign the feature weights via random matrix, which fully explore feature weight relationships to guide the sample adaptation process. Besides, we design a joint loss function with combining the FSL loss and domain adaptive loss for further optimization model. Experiments conducted on several standard hyperspectral datasets demonstrate that the proposed RCASA-FSL is superior to other FSL techniques in both quantitative and qualitative aspects.