Mean shift spectral clustering(MSSC) provides an alternative for clustering tasks. However, due to the time complexity of its embedded mean shift is quadratic scaling in the sample size, the usefulness of MSSC is weakened greatly on large data sets. In this paper, the fast mean shift spectral clustering(FMSSC) algorithm is proposed by replacing parren window estimator(PW) with the fast reduced set density estimator(FRSDE) and combining with the graph-based relaxed clustering(GRC) technique. Compared with MSSC, the asymptotic time complexity of the proposed algorithm is linear with the data size, and the proposed method is straightforward and adaptable.