Acceleration of pickup ions (PUIs) in an environment surrounded by a pair of corotating interaction regions (CIRs) was investigated by numerical simulations using a hybrid code. Energetic particles associated with CIRs have been considered to be a result of the acceleration at their shock boundaries, but recent observations identified the ion flux peaks in the sub‐MeV to MeV energy range in the rarefaction region, where two separate CIRs were likely connected by the magnetic field. Our simulation results confirmed these observational features. As the accelerated PUIs repeatedly bounce back and forth along the field lines between the reverse shock of the first CIR and the forward shock of the second one, the energetic population is accumulated in the rarefaction region. It was also verified that PUI acceleration in the dual CIR system had two different stages. First, because PUIs have large gyroradii, multiple shock crossing is possible for several tens of gyroperiods, and there is an energy gain in the component parallel to the magnetic field via shock drift acceleration. Second, as the field rarefaction evolves and the radial magnetic field becomes dominant, Fermi‐type reflection takes place at the shock. The converging nature of two shocks results in a net energy gain. The PUI energy acquired through these processes is close to 0.5 MeV, which may be large enough for further acceleration, possibly resulting in the source of anomalous cosmic rays.