The variational method, which is a popular approach for image denoising, aims to estimate the original image from a noisy or corrupted image. To consider the constraints of image pixel values fully, our study investigates a constrained second-order total generalized variational (TGV) model, which includes non-negative and bounded constraints as a special case. By adopting an equivalent definition of the second-order TGV, we transform the proposed constrained minimization problem into a minimization of the sum of two convex functions, where one is composed of a linear transformation. Subsequently, we employ the relaxed primal-dual proximity algorithm to solve it. The advantage of the obtained algorithm is that it is matrix-inversion free and does not involve any subproblem. Numerical results demonstrate that the performance of the constrained TGV model is slightly better than that of the unconstrained model.