Tamu Massif

The largest mountain by volume on the planet Earth is a shield volcano that extends from the abyssal plain between Japan and Midway to about two kilometers below the surface of the Pacific Ocean. You can read more about it here:
Tamu Massif

Mauna Loa had long been thought to be the most voluminous mountain on Earth, and still seems to be the biggest with a peak above sea level. Though there are many places with peaks higher above sea level, the great shield volcanoes of the Hawaiian islands are much higher from base to peak than the Himalayas or the Andes. They just start out quite a bit lower. Mauna Kea reaches about 120 feet higher above the Pacific than Mauna Loa, but it's been much less active than its southern cousin in recent years, and as a result most of the bulk of the island of Hawaii is counted as part of Mauna Loa's mass. The mountain complex is in fact nearly the same size as Mars's Olympus Mons, but gravity is much stronger on here than on Mars, and Mauna Kea crushes the bedrock beneath it into a deep furrow in the Pacific Plate. On Mars, where gravity isn't quite so intense, the tops of volcanoes tower well above anything on Earth.

Tamu Massif can't compete with anything in Hawaii, or even the Maldives, when it comes to elevation above sea level, but the mountain is quite impressive when considered relative to the ocean floor. The massif measures over 14,000 feet from base to peak, comparable to the heights of the highest points in California, Colorado, and Washington, though its slope is far more gradual. With slopes rarely greater than one degree, it takes a base the size of New Mexico to reach such a height, and this gives Tamu its edge over Mauna Loa in girth if not in height.

Mauna Loa has been known to people since at least the 6th Century, and to Europeans since the 18th, but Tamu Massiff was not known to be a single mountain until this year. The deep ocean is a thoroughly hostile environment to people, and even at the peak's summit the ambient pressure is 200 times greater than that at the ocean's surface. This makes exploration of the oceans difficult, and it wasn't until significant drilling operations had been conducted throughout the region that the basalt of the massif could be shown to have a single source. Earth is much better explored and better understood than any other planet in the universe, but clearly we have a long way to go before we can say that our homeland is fully explored.