Not quite- time literally slows down in high levels of gravity. You cannot actually experience the slower time, though, because you are slowed down as well.

You can, however, see that other things are moving faster/slower than you relative to how fast you're going in time. A common explanation is that you take two twins and stick one on a spaceship going near the speed of light for a few years. Once the ship returned, the twin from the ship would be significantly younger than the twin who stayed on Earth.

This effect is why satellites need to resynchronize their clocks, by the way. They use extraordinarily precise mechanisms to keep time extremely accurately, but because they're much further from the center of Earth's gravity well (and thus far less effected by time dilation from Earth's gravity) their clocks run ever so slightly faster than clocks on Earth. As a result, they need to repeatedly adjust their clocks backwards to prevent their clocks rapidly desynchronizing from those on Earth.