In this paper, we propose an optimal peer assignment algorithm on peer-to-peer networks. This algorithm is designed to maximize the quality of transmitting fine-scalable coded content by exploiting the embedding property of scalable coding. To be more realistic, we assume that the requesting peer has a delay constraint to display the content within a certain delay bound, and it also has limited incoming bandwidth. We first use a simple example to illustrate the peer assignment problem, and then formulate this problem as a linear programming problem, followed by a nonlinear programming problem. To efficiently solve the second nonlinear problem, we transform it into a sequence of linear programming problems. Finally, we apply our proposed algorithm to both image and video transmissions in bandwidth-limited environments. Extensive experiments have been carried out to evaluate the complexity and performance of our approach by comparing it with both nonlinear formulation and two heuristic schemes. The results have verified the superior performance of our proposed algorithm.