Although the existing array shape estimation methods using reference sources demonstrate good performance, most of the methods require at least two reference sources 2RS in known locations and the reference sources must be in far field. This communication proposes a simplified subspace fitting method that uses only a single reference source 1RS. In the proposed method, the horizontal and vertical positions of each sensor are modeled by applying fixed intersensor spacing and sensor angles, so that the unknown parameters of the cost function are reduced. Furthermore, the Cramer-Rao lower bound (CRLB) is investigated for the proposed method. The results of the numerical experiments indicate that the proposed method is practical for estimating the shape of a towed array.