Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$ when $p$ increase with $n$ has been considered by some authors recently. This model has known an increasing popularity due to its widely applications in multi-user multiple-input single-output (MISO) systems and robust signal processing. In this paper, for more convenient applications in practice, we will investigate the spectral distribution of $\mathbf S_n$ under milder moment conditions than existing work. We also discuss a potential application in sample classification.