Using first-principles calculations and deformation potential theory, we investigate the intrinsic carrier mobility (mu) of monolayer MoS2 sheet and nanoribbons. In contrast to the dramatic deterioration of mu in graphene upon forming nanoribbons, the magnitude of mu in armchair MoS2 nanoribbons is comparable to its sheet counterpart, albeit oscillating with ribbon width. Surprisingly, a room-temperature transport polarity reversal is observed with mu of hole (h) and electron (e) being 200.52 (h) and 72.16 (e) cm(2) V-1 s(-1) in sheet, and 49.72 (h) and 190.89 (e) cm(2) V-1 s(-1) in 4 nm nanoribbon. The high and robust p and its polarity reversal are attributable to the different characteristics of edge states inherent in MoS2 nanoribbons. Our study suggests that width reduction together with edge engineering provide a promising route for improving the transport properties of MoS2 nanostructures.