We calculate particle acceleration during coronal mass ejection (CME) eruptions using combined magnetohydrodynamic and test-particle models. The 2.5D/3D CMEs are generated via the breakout mechanism. In this scenario a reconnection at the "breakout" current sheet (CS) above the flux rope initiates the CME eruption by destabilizing a quasi-static force balance. Reconnection at the flare CS below the erupting flux rope drives the fast acceleration of the CME, which forms flare loops below and produces the energetic particles observed in flares. For test-particle simulations, two times are selected during the impulsive and decay phases of the eruption. Particles are revealed to be accelerated more efficiently in the flare CS rather than in the breakout CS even in the presence of large magnetic islands. Particles are first accelerated in the CSs (with or without magnetic islands) by the reconnection electric field mainly through particle curvature drift. We find, as expected, that accelerated particles precipitate into the chromosphere, become trapped in the loop top by magnetic mirrors, or escape to interplanetary space along open field lines. Some trapped particles are reaccelerated, either via reinjection to the flare CS or through a local Betatron-type acceleration associated with compression of the magnetic field. The energetic particles produce relatively hard energy spectra during the impulsive phase. During the gradual phase, the relaxation of magnetic field shear reduces the guiding field in the flare CS, which leads to a decrease in particle energization efficiency. Important implications of our results for observations of particle acceleration in the solar coronal jets are also discussed.