Multicast routing in high speed networks is one of the key issues in the design and implementation of applications such as video conferencing. Traditionally, the problems are formalised as either the shortest path problem or Steiner tree problem where the objective function is either the shortest path or the minimum costs associated with the path. Furthermore, the problems of multicast routing are usually line problems in the sense that the set of multicast requests to which the network is subject is static and is give in prior. In this paper, we study an online multicast routing problem in Clos network with two optimizing criteria: network throughput and quality of service (or QOS). We propose five routing algorithms according to five system measures using as routing indices. The problem to find an optimal routing according to each of these system measures corresponds to an off-line routing problem. We prove that all of these off-line routing problems except the least-busy routing problem (LB) are NP-complete. We also conduct a series of simulation experiments to study the system performance, namely, the network throughput and QOS, using these routing algorithms as on-line algorithms. The simulation results indicates that the routing algorithms have little impact on the network throughput, but have major impact on the QOS. The LB, the linear time algorithm, outperforms other algorithms while used as on-line routing algorithms as far as the QOS is concerned.