  In this paper we will study the double zeta values $\zeta(k,m)$ using
Picard-Fuchs equation. We will give a very efficient method to evaluate
$\zeta(k,1)$ (resp. $\zeta(k,2)$) in terms of the products of zeta values
$\zeta(2),\zeta(3),\cdots$ when $k$ is even (resp. odd), which admits immediate
generalization to arbitrary double zeta values. Moreover, this method provides
new insights into the nature of double zeta values, which further can be
generalized to arbitrary multiple zeta values.
