A new neural network system for object recognition is proposed which is invariant to translation, scaling and rotation. The system consists of two parts. The first is a preprocessor which obtains projection from the input image plane such that the projection features are translation and scale invariant, and then adopts the Rapid Transform which makes the transformed outputs rotation invariant. The second part is a neural net classifier which receives the outputs of preprocessing part as the input signals. The most attractive feature of this system is that, by using only a simple shift invariant transformation (Rapid transformation) in conjunction with the projection of the input image plane, invariancy is achieved and the system is of reasonably small size. Experiments with six geometrical objects with different degrees of scaling and rotation shows that the proposed system performs excellent when the neural net classifier is trained by the Cascade-correlation learning algorithm proposed by Fahlman and Lebiere.