As a novel clustering method, affinity propagation (AP) clustering can identify high-quality cluster centers by passing messages between data points. But its ultimate cluster number is affected by a user-defined parameter called self-confidence. When aiming at a given number of clusters due to prior knowledge, AP has to be launched many times until an appropriate setting of self-confidence is found. K-AP algorithm overcomes this disadvantage by introducing a constraint in the process of message passing to exploit the immediate results of K clusters. The key to K-AP clustering is constructing a suitable similarity matrix, which can truly reflect the intrinsic structure of the dataset. In this paper, a density-adaptive similarity measure is designed to describe the relations between data points more reasonably. Meanwhile, in order to solve the difficulties faced by K-AP algorithm in high-dimensional data sets, we use the dimension reduction method based on spectral graph theory to map the original data points to a low-dimensional eigenspace and propose a density-adaptive AP clustering algorithm based on spectral dimension reduction. Experiments show that the proposed algorithm can effectively deal with the clustering problem of datasets with complex structure and multiple scales, avoiding the singularity problem caused by the high-dimensional eigenvectors. Its clustering performance is better than AP clustering algorithm and K-AP algorithm.