Named Data Networking (NDN) is considered as a prominent architecture towards future Wireless Local Area Networks (WLAN), and multicast plays an important role in data delivery such as media streaming, multipoint videoconferencing, etc. However, to achieve high-efficiency multicast in NDN WLAN is challenging for two significant reasons. First, without feedback mechanism in IEEE 802.11 standards, to guarantee reliability, the current multicast scheme transmits the multicast data with the basic rate (e.g., 1 Mbps for IEEE 802.11b), which inevitably increases the transmission delay for high-speed consumers. Second, as a NDN multicast group is constituted by consumers who are requesting the same content, multicast groups are easy to form and evolve rapidly, where a data rate adaptation scheme is requisite to accommodate differential multicast groups. In this paper, we propose a multi-stage multicast rate adaptation scheme for NDN WLAN, named NDN-MMRA , to minimize the total transmission time with reliability guarantee for multicast group members. In NDN-MMRA , by checking the Pending Interest Table (PIT) status information, the number of consumers in each multicast group as well as their receiving capabilities are known ahead; with the available data rates in a specific 802.11 standard, NDN-MMRA determines: 1) how many transmission stages are required; and 2) in each stage, which data rate should be adopted. The merit is that with multi-stage transmissions, the data rate can be adapted in descending order to accommodate high-speed consumers with delay minimized, and low-speed consumers with reliability guaranteed. We implement NDN-MMRA in NS-3 by adopting the ndnSIM module, and conduct extensive experiments to demonstrate its efficacy under different IEEE 802.11 standards and various underlying WLAN topologies.