What is the fastest growing plant by amount of carbon stored in the wood? Bamboo is one of the fastest growing woody plants (by height), but it is mostly hollow, and so I'm not sure that it stores that much carbon, relative to other plants.
Ecologists refer to this as 'gross productivity' and define it to be dry weight plant matter per area per year.
In temperate climates this is likely to be a grass. Switchgrass has been proposed as a bio feedstock, both because it's highly productive, and the plant pulls most of the necessary trace nutrients back into the roots in fall.
Poplar and willow are two other bio feedstocks. They reach maximum productivity when coppice grown, and harvested when stems are about 1" thick. (Grow on about 6" spacing)
If you aren't limited to land use, you can likely do better with algae. They produce very fast, but also decompose fast. You have to figure out some way to rapidly harvest the biomass, and remove enough water to frustrate the bacteria. This may make it an impractical solution.
(One of the proposed solutions to carbon sequesterization is to 'fertilize' the oceans with iron. In most water this is the limiting element. The notion is to create an algae bloom. When the algae die, their corpses settle to the abysal plain where decomposition is very slow. So far the experiments to test this aren't conclusive.)
One way to look at it to compare like with like is to look at the photosynthetic efficiency since carbon is fixed through photosynthesis.
By this measure, sugar cane comes on top, converting about 8% of the incomming sunlight energy into stored carbon energy.
Since grass and switchgrass already been mentioned; Hemp and Paulownia tree may be the alternative answer. They are among the fastest growing plants.
For hemp, one unit land area of hemp(s) can produces as much cellulose as 4 unit land area of trees.