What is a superpower?
Superpower is a term used during the cold war to describe the emergence of the USA and USSR as the two foremost great powers.
What is a great power?
A great power is a power which can project military strength globally, exerts global political hegemoney, is recognised as a great power by other great powers and is in the first rank of nations worldwide.
This last part is what made the term superpower contentious in international relations (as opposed to colloquial usage). The great powers are widely recognised as being the permanent members of the UN security council - ie. USA, UK, France, China and Russia, with the possible inclusion of Japan and Germany who fulfill all the criteria of great powers except military strength.
Now it's obvious that since the fall of the USSR (even before that arguably) the USA is by far the most powerful country in the world. Politically, economically and militarily it is the centre of the world. Now by the original definition of great powers, this means it is the only great power, since it is in a class of its own.
China is a powerful regional power with global economic clout. It has growing influence in Africa and the Middle-East and some legacy influence in parts of Latin America. However it is not politically on a par with the USA, not even on a par with smaller countries such as Germany and the UK.
Economically it is very strong, but that economy is based largely on it's industrial capacity. It's per-capita income is still very low and it's human development index barely rates it as an OECD nation never mind in the first rank globally.
In terms of military power, the vast bulk of Chinese military expenditure is focused defensively. Despite being the second or third biggest spender on arms globally, it has a big catch up game to play with the USA and their Western allies. It's technology is lacking and it hasn't got the naval or air capacity to fight a war abroad. For example, China would logistically struggle to attack Iraq in the way the USA did, if it wanted to do such a thing. It lacks the ability to win an air war abroad, and is largely a local power.
So no, China isn't a superpower. It's an emerging great power which may some day reach a position where it's per capita income, military strength and foreign influence ranks it at a par with the USA. But that isn't going to be for a long time yet.
disclaimer: I'm not American