Self-propelled directional liquid transport (SDLT) has been observed on many natural substrates, serving as an efficient strategy to utilize surrounding liquids for a better habitat to the local environment. Drawing inspiration, various artificial materials capable of SDLT have been developed. However, the liquid transport velocity is normally very low (ca. 3-30 mu m/s), which limits its practical applications. Herein, we developed novel pyramid-structured fibers with concave curved surfaces (P-concave curved-fiber, PCCF), which enable the ultrafast SDLT. Specifically, the liquid transport velocity can be up to similar to 28.79 mm/s on a dry tri-PCCF, over 50 times faster than that on the surface of Sarracenia trichome (similar to 520 mu m/s). The velocity is even faster on a wet fiber by two times (similar to 47.34 mm/s). Here, the Laplace pressure difference (FL) induced by the tapered structure determines the liquid transport direction. It is proposed that both the capillary rises imparted by the concave curved surfaces and the oriented microridges/valleys and the enhanced FL aroused by the reduced cross-sectional area accelerate the SDLT on surfaces of the PCCFs. Consequently, the PCCF takes a different liquid transport strategy with a convex-shaped advancing meniscus, differing from that on traditional conical fibers. Moreover, the as-developed PCCF is also applicable for underwater ultrafast SDLT of oil. We envision that the result will open a new perspective for fabricating a fibrous system for microfluidic and liquid manipulation.