Abstract: In the paper,a improved form of the fully conservative finite difference schemes, established by Samarski and Popov(2), for gas dynamics equations in Lagrangian form is presented. To check the quality of the improved scheme, two problems are computed. The first test problem is the typical shock tube problem used by Sod(3). Then the flow fields in a large Shock tube of variable cross sectional ares(4) is computed. The numerical results show that the improved scheme is more efficient than Samarski and Popov's schemes. Meanwhile the nonphysical oscillation and the numerical dissipation also are reduced.