The optimal multicast tree problem in the Software-Defined Networking (SDN) multicast routing is an NP-hard combinatorial optimization problem. Although existing SDN intelligent solution methods, which are based on deep reinforcement learning, can dynamically adapt to complex network link state changes, these methods are plagued by problems such as redundant branches, large action space, and slow agent convergence. In this paper, an SDN intelligent multicast routing algorithm based on deep hierarchical reinforcement learning is proposed to circumvent the aforementioned problems. First, the multicast tree construction problem is decomposed into two sub-problems: the fork node selection problem and the construction of the optimal path from the fork node to the destination node. Second, based on the information characteristics of SDN global network perception, the multicast tree state matrix, link bandwidth matrix, link delay matrix, link packet loss rate matrix, and sub-goal matrix are designed as the state space of intrinsic and meta controllers. Then, in order to mitigate the excessive action space, our approach constructs different action spaces at the upper and lower levels. The meta-controller generates an action space using network nodes to select the fork node, and the intrinsic controller uses the adjacent edges of the current node as its action space, thus implementing four different action selection strategies in the construction of the multicast tree. To facilitate the intelligent agent in constructing the optimal multicast tree with greater speed, we developed alternative reward strategies that distinguish between single-step node actions and multi-step actions towards multiple destination nodes.