Abstract: Let \X_n,n\geq1\ be a \wt\rho-mixing random variable sequence. By using the truncation method of random variables and three series theorem of \wt\rho-mixing sequence, the convergence properties of \wt\rho-mixing sequence are discussed, and a class of strong limit theorems for \wt\rho-mixing sequence are obtained, which generalize the corresponding results of independent sequence. At last, the strong stability for weighted sums of \wt\rho-mixing sequence is studied