A new local density and relative distance based spectrum clustering (LDRDSC) algorithm is proposed to solve multidimensional data clustering in this paper.The density spectra consider both redefined local densities and relative distances.The spectral peaks are regarded as cluster centers since these peaks correspond to the local density maximum.Different clusters corresponding to different spectra, characterized by different colors.The very recently published CFSFDP (Clustering by Fast Search and Find of Density Peaks) algorithm and several benchmark data sets are employed to validate our newly proposed LDRDSC algorithm.Once the density spectrum is generated, the rest points can be automatically clustered by our LDRDSC algorithm.The CFSFDP needs to categorize the rest points according to the cluster centers.Furthermore, our LDRDSC algorithm is compared with four typical clustering algorithms, i.e., DBSCAN,FCM, AP and k-means in order to test the effectiveness of the proposed approach.Computational results demonstrate that our algorithm can obtain better clustering than above mentioned algorithms, especially in identifying noises or isolates.