For the system of adaptive signal processing，the practical application of an algorithm is often limited by its convergence. Thus，it is necessary for a complete algorithm to involve the convergence analysis. In this paper，using the theory of nonliner numerical analysis，the convergence condition is derived for a new algorithm，the Weighted Covariance Estimation (WCE), developed by D.F.Delong^[1] in 1979. Thereof，it is proved theoretically that the convergence of the WCE algorithm is independent of the choice of initial value. This conclusion is verified by the authors from the numerical results obtained through the investigation of computer simulation.