Clustering classifies data into homogeneous groups such that the objects in each group are similar and the objects between groups are not similar. Cluster algorithms can be available in many literatures. And among them, spectral clustering (SC) is one of the most popular and appealing clustering methods because of its generality, efficiency and its rich theoretical foundation. But SC algorithms need cluster number k firstly and use the top k eigenvectors of some affinity matrix as the relaxed version of the cluster result which may have no guarantee on the quality of the solution. In this paper, we explore an effective GA-based clustering algorithm for unknown k with special genetic mechanism. The feature of our proposed method is that the k can be determined as part of cluster process automatically and it can improve cluster result of SCs in term of accuracy. Experimental results illustrate the effectiveness of the proposed method.