Intrigued by the discovery of high-temperature superconductivity in a single unit-cell layer of FeSe film on SrTiO_{3}, researchers recently found large superconductinglike energy gaps in K-adsorbed multilayer FeSe films by angle-resolved photoemission and scanning tunneling spectroscopy. However, the existence and nature of the high-temperature superconductivity inferred by the spectroscopic studies has not been investigated by measurements of zero resistance or the Meissner effect due to the fragility of K atoms in air. Using a self-developed multifunctional scanning tunneling microscope, we succeed in observing the diamagnetic response of K-adsorbed multilayer FeSe films, and thus find a dome-shaped relation between the critical temperature (T_{c}) and K coverage. Intriguingly, T_{c} exhibits an approximately linear dependence on the superfluid density in the whole K adsorbed region. Moreover, the quadratic low-temperature variation in the London penetration depth indicates a sign-reversal order parameter. These results provide compelling information towards further understanding of the high-temperature superconductivity in FeSe-derived superconductors.