Utilizing the first-order spectral graph convolution to explore the correlation between category labels is a common method for multi-label image recognition. However, more graph convolution layers are prone to over-smoothing, hence, employing the first-order spectral graph convolution to directly explore label correlation has some limitations. With respect to the aforementioned problem, a multi-label image recognition method based on adaptive multi-scale graph convolutional network is proposed. The main idea is as follows, the spectral graph convolution in the form of block Krylov subspace is employed to mine the correlation between category labels, and the multi-scale information eixsted in the convolutional layer is spliced and extended to the deep structure, at the same time, the classifier is learned on the relation graph constructed by the adaptive label relation graph module, accordingly the multi-label image recognition is performed more effectively. Experimental results on two public datasets PASCAL VOC 2007 and MS-COCO 2014 verify the effectiveness of the proposed method.