  We study higher syzygies of a ruled surface $X$ over a curve of genus $g$
with the numerical invariant $e$. Let $L \in {Pic}X$ be a line bundle in the
numerical class of $aC_0 +bf$. We prove that for $0 \leq e \leq g-3$, $L$
satisfies property $N_p$ if $a \geq p+2$ and $b-ae \geq 3g-1-e+p$ and for $e
\geq g-2$, $L$ satisfies property $N_p$ if $a \geq p+2$ and $b-ae\geq 2g+1+p$.
By using these facts, we obtain Mukai type results. For ample line bundles
$A_i$, we show that $K_X + A_1 + ... + A_q$ satisfies property $N_p$ when $0
\leq e < \frac{g-3}{2}$ and $q \geq g-2e+1 +p$ or when $e \geq \frac{g-3}{2}$
and $q \geq p+4$. Therefore we prove Mukai's conjecture for ruled surface with
$e \geq \frac{g-3}{2}$. Also we prove that when $X$ is an elliptic ruled
surface with $e \geq 0$, $L$ satisfies property $N_p$ if and only if $a \geq 1$
and $b-ae\geq 3+p$.
