In a conventional PET scanner, coincidence events are limited by the energy window for detection of photoelectric events. In contrast, Compton scatter events occur both in a patient and in detector crystals. Scatter events within the patient cause scatter coincidences, but scatter events within crystals have useful information for an activity distribution. The PET scanner with an extended energy window has higher sensitivity but higher scatter fraction than the PET scanner with a default energy window. In this work, we develop a scatter reduction method using a depth-of-interaction (DOI) detector. The DOI detector can make an upper layer act as an absorber of patient scatter, thus shielding a lower layer. Therefore, Compton scatter events with an interaction at the lower layer mainly have more crystal scatter events than patient scatter events. Our method proposes a different energy window for each layer. The energy window of the upper layer is limited to the region of photopeak events, the same as done for the conventional PET scanner. The energy window of the lower layer is extended to the region of crystal scatter events and photopeak events. We tested our proposed technique for a whole-body PET scanner using GATE simulations. Simulation results show the DOI-PET scanner can provide more true events while keeping a low scatter fraction using our scatter reduction method. We conclude this method is promising for obtaining high image quality using DOI information and energy information.