  In this note, we deduce an asymptotic formula for even power moments of
Kloosterman sums based on the important work of N. M. Katz on Kloosterman
sheaves. In a similar manner, we can also obtain an upper bound for odd power
moments. Moreover, we shall give an asymptotic formula for odd power moments of
absolute Kloosterman sums. Consequently, we find that there are infinitely many
$a\bmod p$ such that $S(a,1;p)\gtrless0$ as $p\rightarrow+\infty.$
