In the aftermath of a hurricane, humanitarian logistics plays a critical role in delivering relief items to the affected areas in a timely fashion. This paper proposes a novel stochastic lookahead framework that implements a two-stage stochastic programming model in a rolling horizon fashion to address the evolving uncertain logistics system state during the post-hurricane humanitarian logistics operations. The two-stage stochastic programming model that executes in this rolling horizon framework is formulated as a mixed-integer programming problem. The model aims to minimize the sum of transportation and social costs. The social cost is measured as a function of deprivation for unsatisfied demand. Our extensive numerical experiment results and sensitivity analysis demonstrate the effectiveness of the proposed approach in reducing the total cost incurred during the post-hurricane relief logistics operations compared to the two-stage stochastic programming model implemented in a static approach.