KNU Advanced Positronium Annihilation Experiment (KAPAE) aims to detect visible rare positronium decay, search for C, CP, and CPT violations as well as search for invisible decay. The KAPAE Phase II is designed to increase the sensitivity of the invisible decay of the positronium such as milli-charged particles, mirror world, new light X-boson, and extra dimensions. Compared to KAPAE phase I, the detector is less segmented, the trigger of the detector is changed to reduce the dead area, and the size of the BGO scintillation crystal and the size of the overall detector is increased. The KAPAE phase II detector consists of BGO scintillation crystals stacked in a 10 by 10 array coupled with SiPM arrays. We show the design of the KAPAE phase II detector and the sensitivity of the invisible decay of the detector using the Geant4 Monte-Carlo simulation. Furthermore, we will report the performance of the detector optimization.