The performance of a desalination membrane depends on a specific pore size suitable for both water permeability and salt rejection. To increase membrane permeability, the applied pressure should be increased, which creates the need to improve membrane stability. In this research article, a molecular dynamics (MD) simulation was performed using ReaxFF module from Amsterdam Modeling suite (AMS) software to simulate water desalination efficiency using a single and multi-layer graphene membrane. The graphene membrane with different pore sizes and a multi-layer graphene membrane with descending pore size in each layer were designed and studied under different pressures. The stability of the membrane was checked using Material Studio 2019 by studying the dynamics summary. The single-layer graphene membrane was evaluated under pressures ranging from 100 to 500 MPa, with the salt rejection ranging from 95% to 82% with a water permeability of 0.347 × 10-9 to 2.94 × 10-9 (mm.g.cm-2s-1.bar-1), respectively. Almost 100% salt rejection was achieved for the multi-layer graphene membrane. This study successfully demonstrated the design and optimization of graphene membrane performance without functionalization.