Because of the powerful mapping ability, back propagation neural network (BP-NN) has been employed in computer-aided product design (CAPD) to establish the property prediction model. The backward problem in CAPD is to search for the appropriate structure or composition of the product with desired property, which is an optimization problem. In this paper, a global optimization method of using the alpha BB algorithm to solve the backward problem is presented. In particular, a convex lower bounding function is constructed for the objective function formulated with BP-NN model, and the calculation of the key parameter alpha is implemented by recurring to the interval Hessian matrix of the objective function. Two case studies involving the design of dopamine beta-hydroxylase (DbetaH) inhibitors and linear low density polyethylene (LLDPE) nano composites are investigated using the proposed method.