We have developed a Monte Carlo event generator for non-resonant diphoton ($gammagamma$) production at hadron collisions in the framework of GR@PPA, which consistently includes processes having additional one jet radiation. The possible double count problem in the generation of radiative processes is avoided by using the LLL subtraction method that we have applied to the weak-boson production processes. The subtraction method has been extended to the final-state QED divergence that appears in the $qg rightarrow gammagamma + q$ process. Because a parton shower (PS) which regularizes the subtracted QED divergence is still under development, we tried to use PYTHIA for the generation of the fragmentation events to restore the subtracted components. The simulation employing the old PS of PYTHIA shows a reasonable matching with the GR@PPA events, and the combined event sample shows a result in reasonable agreement with ResBos. We found that the contribution from $qg rightarrow gammagamma + q$ is significant in the LHC condition. This event generator must be useful for the background studies in low-mass Higgs boson searches at LHC.