Since a fiber volume fraction and a fiber orientation angle have an important effect on elastic coefficients and strengths of carbon fiber reinforced plastics (CFRP), they are main design variables of unidirectional and angle-ply CFRP. However, it is hard to determine the correct values of these variables in the case of designing CFRP plates having specific values of elastic coefficients and strengths. This decision becomes, so to speak, an inverse problem. This paper presents an application of a neural network to the design of elastic coefficients of CFRP and gives the unique solution of this inverse problem by use of the neural network.