In this paper, we proposed a recurrent neural network to compute the distance between a point to an ellipsoid in n spatial dimensions. So far, the problem used to be solved by traditional mathematical algorithms, which is either too slow in computing time or too one-sided in applications. Our proposed neural network, which makes use of a cost gradient projection onto the tangent space of the constraints, not only suitable for the two dimensions problems and three dimensions problems but also can compute the distance from a point to a hyperellipsoid. The numerical results shows that the proposed method is efficient and effective.