Aiming at the problems that current few-shot learning algorithms are prone to overfitting and insufficient generalization ability for cross-domain cases, and inspired by the property that reservoir computing (RC) does not depend on training to alleviate overfitting, a few-shot image classification method based on reservoir computing (RCFIC) is proposed. The whole method consists of a feature extraction module, a feature enhancement module and a classifier module. The feature enhancement module consists of a RC module and an attention mechanism based on the RC, which performs channel-level enhancement and pixel-level enhancement of the features of the feature extraction module, respectively. Meanwhile, the joint cosine classifier drives the network to learn feature distributions with high inter-class variance and low intra-class variance properties. Experimental results indicate that the algorithm achieves at least 1.07% higher classification accuracy than the existing methods in Cifar-FS, FC100 and Mini-ImageNet datasets, and outperforms the second-best method in cross-domain scenes from Mini-ImageNet to CUB-200 by at least 1.77%. Meanwhile, the ablation experiments verify the effectiveness of RCFIC. The proposed method has great generalization ability and can effectively alleviate the overfitting problem in few-shot image classification and solve the cross-domain problem to a certain extent.