The intrinsic acoustic-phonon-limited carrier mobility (μ) of Al2C monolayer sheet and nanoribbons are investigated using ab initio computation and deformation potential theory. It is found that the polarity of the room-temperature carrier mobility of the Al2C monolayer is direction-dependent, with μ of electron (e) and hole (h) being 2348 and 40.77 cm(2)/V/s, respectively, in the armchair direction and 59.95 (e) and 705.8 (h) in the zigzag direction. More interestingly, one-dimensional Al2C nanoribbons not only can retain the direction-dependent polarity but also may entail even higher mobility, in contrast to either the graphene nanoribbons which tend to exhibit lower μ compared to the two-dimensional graphene or the MoS2 nanoribbons which have reversed polarity compared to the MoS2 sheet. As an example, the Al-terminated zigzag nanoribbon with a width of 4.1 nm exhibits μ of 212.6 (e) and 2087 (h) cm(2)/V/s, while the C-terminated armchair nanoribbon with a width 2.6 nm exhibits μ of 1090 (e) and 673.9 (h) cm(2)/V/s; the C-terminated zigzag nanoribbon with a width 3.7 nm exhibits μ of 177.6 (e) and 1889 (h) cm(2)/V/s, and the Al-terminated armchair nanoribbon with a width 2.4 nm exhibits μ of 6695 (e) and 518.4 (h) cm(2)/V/s. The high carrier mobility, μ, coupled with polarity and direction dependence endows the Al2C sheet and nanoribbons with unique transport properties that can be exploited for special applications in nanoelectronics.