Wireless multimedia traffic has increased considerably in recent years, which puts forward higher demand on the capacity of existing network. Multicast, as a transmission strategy with high spectral efficiency, has not been widely studied in heterogeneous cellular network (HetNet). In this paper, we propose a QoS-based multi-rate multicast scheme over HetNet to effectively improve the system throughput while guaranteeing the quality of service (QoS) of the whole system. We formulate an expression of system throughput of the proposed multicast scheme and decouple it into three subproblems for its computational complexity, namely, user association (UA), subgroup formation (SF) and resource allocation (RA). In UA, we present a traffic-oriented access method based on reference signal receiving power (RSRP). In SF, the associated users are divided into several subgroups according to their channel state information (CSI) and the users in one subgroup are served with the same rate determinated by the CSI level of the subgroup. In RA, fractional frequency reuse (FFR) mechanism is used to eliminate the co-channel cross-tier interference between macro base station (MBS) and small base stations (SBS). And QoS is considered both in subcarrier allocation and power allocation processes. Simulation results show that the system throughput is significantly improved while QoS is guaranteed by using our scheme.