Arrayed waveguide grating is a versatile and scalable integrated light dispersion device, which has been widely adopted in various applications, including, optical communications and optical sensing. Recently, thin-film lithium niobate emerges as a promising photonic integration platform, due to its ability of shrinking largely the size of typical lithium niobate based optical devices and possible integration of them on a chip. However, due to the intrinsic anisotropy of the material, to build an arrayed waveguide grating on X-cut thin-film lithium niobate has never been successful. Here, a universal strategy to design anisotropy-free dispersive components on a uniaxial in-plane anisotropic photonic integration platform is introduced for the first time. This leads to the first implementation of arrayed waveguide gratings on X-cut thin-film lithium niobate with various configurations and high-performances. The best insertion loss of 2.4dB and crosstalk of -24.1dB is obtained for the fabricated arrayed waveguide grating devices. Applications of such arrayed waveguide gratings as a wavelength router and in a wavelength-division multiplexed optical transmission system are also demonstrated.