Let {Xn,n ≥1}be a stationary sequences of for a ∗-mixing process with distribution function F(x) = P[X1 ≤ x]. A wavelet linear distribution function Fn(x) based on X1,X2,...,Xn is introduced. We establish that the strong consistency and pointwise as well as uniform convergence of Fn(x)are the same as empirical distribution function. In contrast to easy computing of empirical distribution function, the estimation based on wavelets are smooth and could be differentiable which is more convenient for forecasting.