Utilization of bioenergy with carbon capture can realize carbon-negative syngas production. The quadruple fluidized bed gasifier (QFBG) integrates a chemical looping oxygen generation process and a dual fluidized bed gasifier with limestone as bed material. It is one promising device that can convert biomass to H2-rich syngas whilst capturing CO2 with little energy penalty. However, experimental or numerical simulation of QFBG is rarely reported on due to its complex structure, hindering the further commercialization and deployment of QFBG. In this work, a new computational fluid dynamics (CFD) solver is proposed to predict the complex physicochemical processes in QFBG based on the multi-phase particle in cell (MPPIC) methodology with the assistance of the open source software, OpenFOAM. The solver is first validated against experimental data in terms of hydrodynamics and reaction kinetics. Then, the solver is used to investigate the QFBG property. It is found that the QFBG can operate stably. The cold gas efficiency, H2 molar fraction, and CO2 capture rate of the QFBG are predicted to be 87.2%, 93.3%, and 90.5%, respectively, which is promising. It is believed that the solver can give reliable predictions for similar fluidized bed reactors.