Frame coefficients play an important role in the study of frame theory, which helps in the structural analysis of applications for frames. However, we know very little about the distribution of frame coefficients sequences. In this paper, we mainly study the distribution of the frame coefficients for vectors in a Hilbert space by using the minimum eigenvalue of frame operator. Our results generalize and improve the remarkable results which have been obtained by Brewaster et al. Finally, we present some examples to demonstrate the efficiency of our conclusions.