  In this paper we compute the mapping class group of closed simply-connected
6-manifolds $M$ which look like complete intersections, i.~e.~ $H_2(M;\mathbb
Z) \cong \mathbb Z $ and $x^3 \ne 0$ where $x \in H^2(M; \mathbb Z)$ is a
generator. We determine some algebraic properties of the mapping class group;
for example we compute its abelianization and its center. We show that modulo
the center the mapping class group is residually finite and virtually
torsion-free. We also study low dimensional homology groups. The results are
very similar to the computation of the mapping class group of Riemann surfaces.
We give generators of the mapping class group, and generators and relations for
the subgroup acting trivially on $\pi_{3}(M)$.
