The maximum strain rate sensitivity (m) superplastic deformation (MaxmSPD) of Mg-Li based alloys was conducted via realization of the maximum m value throughout the deformation process such that the optimum superplastic deformation (SPD) of materials is obtained. So far, the MaxmSPD has only been successfully applied to titanium alloys, but its potential application in other alloys has not yet been explored and exploited. In this article, the MaxmSPD of Mg-9Li-1Al alloy was investigated by conducting the MaxmSPD and the constant strain rate SPD (CSRSPD) experiments and comparison of the SPD results. The materials with two different statuses were used in the investigation: as-extruded samples extruded from the as-cast material, and the samples with 4- or 8-pass equal channel angular extrusion (ECAE). The MaxmSPD and CSRSPD experiments were conducted at the temperature of 548, 573 and 598K. The maximum elongation is 563.7%, obtained by MaxmSPD at 573K using the 8-pass ECAEed samples. It was found that under certain conditions, the samples exhibit more elongation in MaxmSPD. The microstructure of the samples is examined and compared, and the differences between MaxmSPD and CSRSPD are discussed. The investigation thus provides an in-depth and epistemological understanding of the SPD mechanism of Mg-Li based alloys.