Abstract: In this paper,we consider the estimates σ_m² of error variance σ²=Var(e_i) in the linear models Y_i=x'_iβ+e_i(i=1, 2,…). We study the complete convergence of σ_m²-σ² when the error {e_i }is a sequence of identically distributed φ-mixing variables. And we also obtain the better convergence rates when {e_i} is not identically distribution.