To control premixed charge compression ignition (PCCI) phasing in internal combustion engines, a novel method called high-pressure air jet controlled compression ignition (JCCI) based on compound thermodynamic cycle was proposed to achieve diesel premixed combustion in all load operations. The method is implemented in a hybrid pneumatic engine (HPE). The application of HPE is also beneficial to the fuel consumption and emissions because of its several flexible operation modes. The purpose of this paper is to investigate the in-cylinder high-pressure air JCCI combustion processes in the power cylinder of HPE. A three-dimensional (3D) computational fluid dynamics (CFD) model coupled with reduced n-heptane chemical kinetics has been developed to analyze the effects of high-pressure air jet pressure and temperature on the in-cylinder ignition and combustion characteristics. The results demonstrated that the diesel premixture combustion phasing can be controlled near the top dead center (TDC) with the variations of air jet pressure and temperature. For the combustion characteristics, the local region of the in-cylinder mixture is compressed and ignited by the high-pressure air jet. Intensified low-temperature reaction and two-stage high-temperature reaction can also be observed. Low jet pressure and high jet temperature have the potential of obtaining high efficiency due to the rapid combustion.