We propose a time-sharing based rate adaptation scheme for reliable multicasting over the fading channels in mobile wireless networks. Specifically, the proposed scheme aims at achieving high system throughput/spectral-efficiency by dynamically adjusting the transmission rate according to the variations of channel state information (CSI) of all multicast mobile receivers. First, we formulate the time-sharing based spectral-efficiency optimization problem to obtain the adaptive rate policies. Also, we apply a concatenated error-correction model for reliable mobile multicast. Then, we derive the solution for the optimization problem when the fading channels of multicast receivers are independent and identically distributed (i.i.d.). Also conducted is a set of simulation evaluations which show the performance superiority of our proposed adaptive rate policy over the worst-case SNR-dominating policy and the best-case SNR-dominating policy.