In modern multivariate analysis, the dimensions (columns) p of the data matrix X may be very large compared with the sample size (rows) n.  Many traditional results do not apply to this case. Johnstone (2001, [15]) recently studied the asymptotic distribution for the normalized largest eigenvalue of large sample covariance matrix S. In this talk, we focus on the asymptotic distribution related with the eigenvalues of large dimensional sample correlation matrices R. A new central limit theorem for the traces of large sample correlation matrix was proved by using Random Matrix theory. Its further conjecture on the asymptotic distribution for the normalized largest eigenvalue of large sample correlation matrix is also proposed with an outline of the proof addressed.