Optimization of water distribution networks, regardless of uncertainties of effective variables in design of network is unrealistic. Therefore, developing method based on uncertainties variables in water distribution network design is necessary. In this research, a model based on simulation-optimization approach (combination of genetic algorithm and EPANET software) with fuzzy variables has been developed. Also, water distribution networks without causing disruption in their Performance with level-1 redundant have been optimized. In this model, fuzzy nodal demands and fuzzy available nodal heads are characterised by triangular membership functions. Furthermore, desirable nodal heads are also considered as fuzzy and relationship between fuzzy available nodal heads and fuzzy desirable nodal heads is used to convert fuzzy constraints to crisp constraints. For validation of model, the program has been implemented for optimization of level-1 redundant water distribution single network with fuzzy demands then paid to the optimization Jangal water distribution network with fuzzy demands (under one pipe failure condition) as a case study. The result of this model shows the cost of optimal design of Level-1 redundant water distribution networks model with fuzzy demands regard of scale of network 30% to 70% is increases due to providing nodal heads to offset the one pipe failure condition from network.