This paper deals with a realistic multi-period liner ship fleet planning problem by incorporating stochastic dependency of the random and period-dependent container shipment demand. This problem is formulated as a multi-period stochastic programming model with a sequence of interrelated two-stage stochastic programming (2SSP) problems characterized ship fleet planning in each single period. A solution method integrating dual decomposition and Lagrangian relaxation method is designed for solving the developed model. Numerical experiments are carried out to assess applicability and performance of the proposed model and solution algorithm. The results further demonstrate importance of stochastic dependence of the uncertain container shipment demand.