For a fiber bundle with a finite cohomology dimension and
1
1
-connected base
B
B
and
1
1
-connected fiber
F
F
, we obtain the homology of the section space by an
E
1
{E^1}
-spectral sequence. In the "stable" range the
E
1
{E^1}
-terms are the homology of a product of Eilenberg-Mac Lane space of type
K
(
H
p
−
i
(
B
;
π
p
F
)
,
i
)
K({H^{p - i}}(B;{\pi _p}F),i)
(the same as those of the
E
1
{E^1}
-spectral sequences which converges to the homology of the functional space
Hom
(
B
,
F
)
\operatorname {Hom} (B,F)
[10]). The differential is the product of two operations: one appears in the
E
1
{E^1}
-spectral sequence, which converges to the homology of
Hom
(
B
,
F
)
\operatorname {Hom} (B,F)
; the second one is a "cup-product" determined by the fiber structure of the bundle. This spectral sequence is obtained by a Moore-Postnikov tower of the fiber, which generalizes Kahn’s methods [9].