In this article we study normal generation of irrational ruled surfaces. When
C
C
is a smooth curve of genus
g
g
, Green and Lazarsfeld proved that a very ample line bundle
L
∈
Pic
X
L \in \mbox {Pic}X
with
deg
(
L
)
≥
2
g
+
1
−
2
h
1
(
X
,
L
)
−
Cliff
(
X
)
\mbox {deg}(L) \geq 2g+1-2h^1 (X,L) - \mbox {Cliff}(X)
is normally generated where
Cliff
(
C
)
\mbox {Cliff}(C)
denotes the Clifford index of the curve
C
C
(Green and Lazarsfeld, 1986). We generalize this to line bundles on a ruled surface over
C
C
.