The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D axisymmetric coordinate. The numerical method is based on least-square gridless method,and the inviscid flux is calculated by multi-component HLLC( Harten-Lax-van Leer-Contact) scheme,and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2,and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region,the recirculation zone enlarges and moves downstream,the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0,the rear stagnation point shifts downstream approximate 0. 26 caliber,and the base pressure increases about 53. 4%,and the total drag force coefficient decreases to 0. 182 which agrees well with the trajectory model prediction. Due to neglecting the effects of viscosity and turbulence,there exists a certain difference at Ma = 1. 5,2. 0. The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler’s Equation in 2-D axisymmetric coordinates. The numerical method is based on least-square gridless method, and the inviscid flux is calculated by a multi-component HLLC (Harten-Lax-van Leer-Contact) scheme, and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2, and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region, the recirculation zone enlarges and moves downstream, the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0, the rear stagnation point shift downstream approximate 0. 26 caliber, and the base pressure increases about 53. 4%, and the total drag force co Due to neglecting the effects of viscosity and turbulence, there exists a certain difference at Ma = 1.52. 0.