This paper studies fault-tolerance problem of feedforward neural networks implemented in pattern recognition. Based on dynamical system theory, two concepts of pseudo-attractor and its region of attraction are introduced. A method estimating fault tolerance of feedforward neural networks has been developed. This paper also presents definitions of terminologies and detailed derivations of the methodology. Some preliminary results of case studies using the proposed method are shown, the proposed method has provided a framework and an efficient way for direct evaluation of fault-tolerance in feedforward neural networks.