A graded-index fiber with yttrium aluminosilicate (YAS) glass core was fabricated by a Melt-in-Tube method. The refractive index and stress profiles of the fibers exhibit a highly symmetrical gradient tendency along the radial axis which is in accordance with the results of element migration. Based on the formation mechanism of YAS glass core, the relationships between the refractive index/stress profile and the spontaneous migration are discussed. A linear all-fiber laser based on the obtained fiber shows a laser output threshold of 11.48 mW and slope efficiency of 8.3%. The near-field beam intensity distribution of fiber laser with spectrum FWHM of 0.24 nm indicates the good laser beam quality. The facile Melt-in-tube method was proved to be reliable in designing graded-index fiber through the dissolution and diffusion process, which is more advanced than commonly used Rod-in-tube method.