Light confinement and amplification in micro- & nano-fiber have been intensively studied and a number of applications have been developed. However, the typical micro- & anno- fibers are usually free-standing or positioned on a substrate with lower refractive index to ensure the light confinement and guiding mode. Here we numerically and experimentally demonstrate the possibility of confining light within a microfiber on a high refractive index substrate. In contrast to the strong leaky to the substrate, we found that the radiation loss was dependent on the radius of microfiber and the refractive index contrast. Consequently, quasi-guiding modes could be formed and the light could propagate and be amplified in such systems. By fabricating tapered silica fiber and dye-doped polymer fiber and placing them on sapphire substrates, the light propagation, amplification, and laser behaviors have been experimentally studied to verify the quasi-guiding modes in microfer with higher index substrate. We believe that our research will be essential for the applications of micro- and nano-fibers.