  In this paper, we show that the maximal divisible subgroup of groups $K_1$
and $K_2$ of an elliptic curve $E$ over a function field is uniquely divisible.
Further those $K$-groups modulo this uniquely divisible subgroup are explicitly
computed. We also calculate the motivic cohomology groups of the minimal
regular model of $E$, which is an elliptic surface over a finite field.
