Motivated by modern large-scale information processing problems in engineering, this chapter concentrates on studying distributed constrained convex optimization problems over a connected undirected network. The problem involves a sum of a differentiable convex function with Lipschitz continuous gradient and two nonsmooth convex functions with a linear operator. To solve such a problem, we propose a novel distributed primal-dual forward-backward splitting algorithm, called D-PDFBS. Each agent locally computes the Lipschitz continuous gradient and two proximal operators, and exchanges information with its neighbors. D-PDFBS adopts non-identical step sizes, and we reveal the relationship between selection of step sizes and parameters of objective functions. The simulation results verify the feasibility of D-PDFBS and the correctness of theoretical findings.