The development of high-resolution mesoscale weather forecast numerical models is an important way to improve the forecast of torrential rain. Regional mesoscale models, with a spatial resolution to 100m, pose great challenges to current computational resources. A feasible solution is to develop soundproof models to replace those fully compressible models. Soundproof models permit relatively larger time steps, improving the integration efficiency significantly. We developed a test version of a pseudo-incompressible model in a terrain-following mass-based coordinate (η coordinate), based on a sound-proof theory namely the pseudo-incompressible theory in 2018. Numerical tests indicate the results from the model are reliable. However, a key issue is the acoustic wave not yet excluded by the model. In this paper we improve the pseudo-incompressible model and establish a new dry air dynamic core for the pseudo-incompressible model. The most significant improvement of the governing equations of the new dynamic core is that it solves an elliptic equation for perturbation pressure, which ensures the exclusion of acoustic waves in theory. The improvement in the numerical scheme of the new dynamic core is that the time-integration scheme no longer relies on the time-split algorithm. We compared the simulation results by the improved version of the pseudo-incompressible model with those by WRF model in a dry hot bubble numerical test. It is found that the pseudo-incompressible model obtains similar dynamic and thermodynamic field distributions to those from the WRF model, and the simulated perturbation pressure time series are smooth, indicating that the acoustic waves have been removed. This is a significant improvement over the pseudo-incompressible model released in 2018.