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A new two-way coupled direct numerical simulation (DNS) method is developed to study the turbulence modulation in the compressible and spatial developing particle-laden turbulent jets with higher Reynolds number. The high-resolution solver is performed for the gas phase flow-field and the Lagrangian method is used to trace particles. It is found that the particles with Stokes number of 0.01and 50 advance the evolution of the coherent structures in the flow-field, but the particles with Stokes number of 1 delay it. All particles increase the turbulent kinetic energy and decrease the vorticity thickness, in which the particles with the Stokes number of 1 exhibit the maximum modulation. The jet velocity half-width and the decay of the streamwise mean velocity along the centerline are reduced by particles with Stokes number of 0.01 and 1. The momentum thickness is increased by particles and the larger the Stokes number is, the larger the momentum thickness is.