The liquid crystal (LC)-based open surface microfluidic can manipulate the liquid in micro-nano scale by utilizing microfluidics principles and micromachining techniques, which is crucial for developing next generation microfluidic platforms. In this work, rational theoretical design and controlled synthesis are conducted to prepare anisotropic functional polymer films including nematic and smectic LC polymer films. According to our study, the flow of droplets on nematic LC polymer films is an order of magnitude faster than on smectic LC polymer films. Moreover, both the nematic and smectic LC polymer films can trigger orientation-dependent flow velocity of droplets, which realize the anisotropic transports of droplets and thereby lays a foundation for the development of specific microfluidic technology based on patterned LC functional surfaces.