The adopted cure cycle in the filament winding process must lead to a completely cured composite. However, a restriction on the temperature should be observed to avoid the resin degradation. Here, an optimum cure cycle was determined using a hybrid neural network—first principles model (HNM) of the filament winding process and the particle swarm optimization method to find the minimum of an economic objective function. HNM was based on energy and mass balances, being the cure kinetics described by a neural network model. The results showed a high degree of cure and a shorter processing time with a lesser energy demand. POLYM. COMPOS., 35:1377–1387, 2014. © 2013 Society of Plastics Engineers