Replacing diesel by natural gas in diesel engine is of great interest for transportation and power station industry due to larger availability and lower environmental impact of natural gas compared to diesel fuel. In addition, the high-pressure direct injection (HPDI) natural gas engine is widely recognized as a positive development prospect and an ideal alternative to conventional diesel engine. However, the trade-off relationship between indicated thermal efficiency (ITE) and NOx emissions limits the development of dual-fuel engines. In order to resolve this problem, we established a three-dimensional model combined with a multicomponent reduced chemical kinetic model and a phenomenological soot model. Using the 3D simulation model, we jointly optimized the combustion chamber (CC) structure, diesel/natural gas (NG) injection pressure (IP), and exhaust gas recirculation (EGR) strategy for HPDI NG engine in the two combustion modes. The results show that the adoption of the straight crater type (SCT) CC improves the mixture space equivalent ratio gradient distribution, slightly increases NOx emissions, rises ITE and reduces CO emissions in the two combustion modes. In NG mixture-limited combustion (NMLC) mode, increasing the diesel injection pressure (DIP) while appropriately increasing the NG injection pressure (NIP) promotes multi-point ignition and faster flame propagation and further optimizes CO emissions. In NG slightly premixed combustion (NSPC) mode, high ITE and low CO emissions can be maintained by increasing DIP while slightly increasing NIP, but the NOx increases substantially. In the moderate NOx emissions region (1.0 g/kW·h ∼ 2.0 g/kW·h), as the EGR rate increases, an overall improvement in trade-off relationships of NOx-CO, NOx-soot, and NOx-ITE in NMLC mode can be achieved. In NSPC mode, as the EGR rate increases, although CO and soot emissions can maintain lower values, it is difficult to improve the trade-off relationship of NOx-ITE.