The definition of K-theory of a scheme $X$ is defined as $G_i(X):=K_i(\mathrm{Coh}(X))$ or $K_i(X):=K_i(\mathrm{Vec}(X))$. But usually the schemes are required to be (at least locally) Noetherian, and usually it is said that if it is not then the $G_i$'s are pretty bad.

But for what reasons that we really need the condition of being noetherian? (If it is not, then $\mathrm{Coh}(X)$ is not abelian, but we only need it to be exact, which might be satisfied.)