Hopfield neural networks tolerating weight faults are presented. The weight restriction and fault injection are adopted as fault-tolerant approaches. For the weight restriction, a range to which values of weights should belong is determined during the learning, and any weight being outside this range is forced to be either its upper limit or lower limit. A status of a fault occurring is then evoked by the fault injection, and calculating weights is made under this status. The learning based on both of the above approaches surpasses the learning based on either of them in the fault tolerance and/or in the learning time.