Implicit surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. J\"uttler et al.\cite{Juttler02} proposed an algorithm for fitting implicitly defined algebraic spline surfaces, but it can not represent the detail of the model effectively. Tong et al.\cite{Tong06} proposed a hierarchical implicit surface representation which has good adaptability and is suitable for representing level of detail models. Wang et al.\cite{Wang2011} presented an adaptive surface reconstruction approach based on the implicit PHT-splines which is effective and has the strong adaptability for describing geometric details. But all of the these methods need large storage. In recent years, low rank representation has attracted considerable attention in areas of function approximation, matrix recovery and completion, image processing, signal processing, statistics and machine learning, as it can reduce the dimension of the data. But it is rarely applied in geometric processing and modeling. In this paper, we propose a low-rank separated representation algorithm to solve the surface reconstruction problem---reconstructing a surface from a dense set of point clouds. Our algorithm is driven by surface fitting model proposed in \cite{Tong06}, which is based on the hierarchical implicit tensor-product B-spline representation(HITPBS) of surfaces. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data. At the same time, Low-rank inducing regularization techniques are used in order to exploit the possible low-rank of the implicit spline surface. Then doing CP decomposition of the coefficient tensor, the implicit surface can be expressed as a low-rank separated form. By measuring the fitting errors over each cell of the mesh, then split these cells into eight sub-cells over which the errors are larger than some given threshold and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. In the last, We provide some examples to demonstrate our algorithm and compare it with several existing methods. Examples suggest that our method is able to produce reconstruction surfaces of high quality and the implicit separated representation form is easier to store and use.