In this paper, we propose a constrained least squares approach for stably computing Laplacian deformation with strict positional constraints. In the existing work on Laplacian deformation, strict positional constraints are described using large values of least squares weights, which often cause numerical problems when Laplacians are described using cotangent weights. In our method, we describe strict positional constraints as hard constraints. We solve the combination of hard and soft constraints by constructing a typical least squares matrix form using QR decomposition. In addition, our method can manage shape deformation under over-constraints, such as redundant and conflicting constraints. Our framework achieves excellent performance for interactive deformation of mesh models.