The general position number gp(G) of a graph G is the cardinality of a largest set of vertices S such that no element of S lies on a geodesic between two other elements of S. The complementary prism G
of G is the graph formed from the disjoint union of G and its complement
by adding the edges of a perfect matching between them. It is proved that gp(G
) ≤ n(G) + 1 if G is connected and gp(G
) ≤ n(G) if G is disconnected. Graphs G for which gp(G
) = n(G) + 1 holds, provided that both G and
are connected, are characterized. A sharp lower bound on gp(G
) is proved. If G is a connected bipartite graph or a split graph then gp(G
) ∈ {n(G), n(G)+1}. Connected bipartite graphs and block graphs for which gp(G
) = n(G) + 1 holds are characterized. A family of block graphs is constructed in which the gp-number of their complementary prisms is arbitrary smaller than their order.
