Spacelike and timelike generalized parton distributions (GPDs) have been investigated at charged-lepton accelerator facilities, for example, by the virtual Compton scattering and the two-photon process, respectively. In this work, we show the (pi ^pm ) and (pi ^0) production cross sections in neutrino (antineutrino) reactions (nu ,(bar{nu }) + N rightarrow ell + pi + N') for studying the GPDs of the nucleon by using the theoretical formalism of Pire, Szymanowski, and Wagner. The (pi ^pm )-production cross sections are useful for finding mainly gluon GPDs, whereas the (pi ^0) production probes quark GPDs, although there are sizable quark-gluon interference terms in the (pi ^pm ) production. In particular, we show the roles of the pion- and rho-pole terms, the contribution from each GPD term (H, E, ({tilde{H}}), ({tilde{E}})), the effects of the gluon GPDs (H_g) and (E_g), and the dependence on the energy of the process in the neutrino cross sections. These cross sections could be measured at Fermilab in future. The neutrino GPD studies will play a complementary role to the projects of charged-lepton and hadron reactions for determining the accurate GPDs.