There are no mountains on Jupiter. As one of the solar system's gas giant planets, Jupiter has no solid surface or core. The planet is primarily comprised of hydrogen and helium gas. Terrestrial planets, such as Earth, have solid cores and consist of rock and metal.
While Jupiter itself may not have mountains, one of its moons, Io, does. In fact, Io boasts some of the highest peaks in all of the solar system; Io's Euboea Montes' peak is estimated at 8.3 miles high, which rivals earth's tallest mountain, Mauna Kea, which reaches 6.3 miles. Though in the case of Mauna Kea, the bulk of the mountain is hidden beneath the ocean, so it's visible peak appears much shorter. Either way, in terms of overall height, both make Mt. Everest pale in comparison, with its 2.9 mile-high peak.