Since $S_{n}$ is the sum of the first $n$ terms of an arithmetic sequence $\{a_{n}\}$, and the sum of the odd-numbered terms among the first $2017$ terms of $\{a_{n}\}$ is $2018$,
we have $S_{odd} = a_{1} + a_{3} + a_{5} + \ldots + a_{2017} = 1009 \times (a_{1} + a_{2017}) \times \frac{1}{2} = 2018$, which gives $a_{1} + a_{2017} = 4$.
Then, $S_{2017} = \frac{2017}{2}(a_{1} + a_{2017}) = 2017 \times 2 = 4034$.
Therefore, the answer is $\boxed{4034}$.
This problem examines the formula for the sum of an arithmetic sequence $S_{n} = \frac{n}{2}(a_{1} + a_{n})$. First, by using $S_{odd} = a_{1} + a_{3} + a_{5} + \ldots + a_{2017} = 1009 \times (a_{1} + a_{2017}) \times \frac{1}{2} = 2018$, we find that $a_{1} + a_{2017} = 4$. Then, calculating $S_{2017} = \frac{2017}{2}(a_{1} + a_{2017}) = 2017 \times 2 = 4034$ is straightforward.
This question tests the formula for the sum of an arithmetic sequence and calculation skills, and is considered a medium-level problem.