Network coding is a promising generalization of routing which allows a network node to generate output messages by encoding its received messages to reduce the bandwidth consumption in the network. An important application where network coding offers unique advantages is the multicast network where a source node generates messages and multiple receivers collect the messages. Previous network coding schemes primarily considered encoding the messages in a single multicast session. In this paper, we considerthe linear inter-session network coding for multicast. The basic idea is to divide the sessions into different groups and construct a linear network coding scheme for each group. To maximize the performance, we introduce two metrics: overlap ratio and overlap width, to measure the benefit that a system can achieve by inter-session network coding. The overlap ratio mainly characterizes the network bandwidth while the overlap width characterizes the system throughput. Our simulation results show that the proposed inter-session network coding scheme can achieve about 30%$ higher throughput than intra-session network coding.