The production rate and kinematic distributions of isolated photon pairs produced in hadron interactions are studied. The effects of the initial-state multiple soft-gluon emission to the scattering subprocesses q-qbar, qg, and gg to gamma gamma X are resummed with the Collins-Soper-Sterman soft gluon resummation formalism. The effects of fragmentation photons from qg to gamma q, followed by q to gamma X, are also studied. The results are compared with data from the Fermilab Tevatron collider. A prediction of the production rate and kinematic distributions of the diphoton pair in proton-nucleon reactions is also presented.