As the proportion of video programs is expected to grow significantly, video services will require a huge amount of Internet bandwidth in the future. In this paper, we model the video program placement (VPP) problem in tree networks which sends video programs to the requesting (demand) nodes using a broadcast method. The model considers the cost for both assigning programs to nodes and broadcasting video programs through links. The model is formulated as an integer program, and its objective is to minimize the total cost of VPP in a tree network. We develop a dynamic programming algorithm to solve this problem with time complexity O(NP) where N is the number of nodes and P is the number of video programs.