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A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finiteabelian group, is called quasi-good if each homogeneous component is1-dimensional and 0 is not in the support of the grading.  Analogous to classical root systems, we define a finite root system $R$ to besome subset of a finite symplectic abelian group satisfying certain axioms.There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with aquasi-good grading on it. Thus one can construct nice basis of $L(R)$ by meansof finite root systems.  We classify finite maximal abelian subgroups $T$ in $\Aut(L)$ for complexsimple Lie algebras $L$ such that the grading induced by the action of $T$ on$L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always afinite root system. There are five series of such finite maximal abeliansubgroups, which occur only if $L$ is a classical simple Lie algebra.

Fine gradings of complex simple Lie algebras and Finite Root Systems