Designing an efficient supply chain for organ transplant networks which is intimately related to humans’ life plays a primary role in improving the network’s performance. This research is focused on proposing a new multi-period location-allocation modeling approach to make appropriate strategic decisions for designing organ transplant networks under supply and budget uncertainties. To serve this purpose, a bi-objective possibilistic programming model is formulated the aim of which is to maximize network responsiveness and minimize the total cost. A fuzzy goal programming approach is adopted to solve multiple objective function models and control their deviations from the corresponding aspiration levels. As an important contribution of this study, the chance of success of transplantation processes is taken into consideration by proposing appropriate utility functions according to transportation criteria. Moreover, for the purpose of coping with the inherent uncertainty of the input parameters, a possibilistic programming model based on Me measure converted to three optimistic, realistic and pessimistic models is developed. Three new formulations have also been developed to tackle equality chance constraints. Finally, the optimal solutions of the developed models are analyzed through conducting a real case study in Iran. According to the results, for the considered organ transplant network, the possibilistic programming model based on the realistic measure is better than the optimistic and pessimistic measure in most confidence levels.