To provide constraints on a number of significant controversial issues related to the structure and dynamics of the Australian continent, we utilize P-to-S receiver functions (RFs) recorded by 182 stations to map the 410 and 660 km discontinuities (d410 and d660, respectively) bordering the mantle transition zone (MTZ). The RFs are stacked in successive circular bins with a radius of 1° under a non-plane wave front assumption. The d410 and d660 depths obtained using the 1-D IASP91 earth model show a systematic apparent uplifting of about 15 km for both discontinuities in central and western Australia relative to eastern Australia, as the result of higher seismic wave speeds in the upper mantle beneath the former area. After correcting the apparent depths using the Australian Seismological Reference Model, the d410 depths beneath the West Australia Craton are depressed by ~10 km on average relative to the normal depth of 410 km, indicating a positive thermal anomaly of 100 K at the top of the MTZ which could represent a transition from a thinner than normal MTZ beneath the Indian ocean and the normal MTZ beneath central Australia. The abnormally thick MTZ beneath eastern Australia can be adequately explained by subducted cold slabs in the MTZ. A localized normal thickness of the MTZ beneath the Newer Volcanics Province provides supporting evidence of non-mantle-plume mechanism for intraplate volcanic activities in the Australian continent.