A multi-period mean-variance portfolio selection problem with stochastic investment horizon in the financial market where the market states are partially observable is considered. Suppose that the dynamics of the unobservable market states is described by a finite-state discrete-time hidden Markov chain. Return of the risk-free asset is assumed to depend on the observable market state at that period. And return of the risky asset is assumed to be dependent both on the observable and unobservable market states at that period. The portfolio selection optimization problem with partially observable information is transformed into the optimization problem with fully observable information by using the method of sufficient statistics. And explicit expressions of optimal portfolio strategy and efficient frontier are derived by adopting dynamic programming approach and Lagrange dual theory.