The standard Markowitz Mean-Variance optimization model is a single-period portfolio selection approach where the exit-time (or the time-horizon) is deterministic. In this paper the Mean-Variance portfolio selection problem has been studied with uncertain exit-time when each asset has individual uncertain exittime, which generalizes the Markowitz's model. Some conditions are provided under which the optimal portfolio of the generalized problem is independent of the exit-times distributions. Also, it is shown that under some general circumstances, the sets of optimal portfolios in the generalized model and the standard model are the same.