In this paper, generalized from some monotone scheme, a class of MUSCL- Type finite difference E schemes is presented. It is proved to have second order accuracy both in space and time. And applying the theory of entropy measure- valued solution, we proved the family of approximate solutions converge to the unique entropy weak l∞ -solution. Based on the character in 1-D,the convergence to the unique entropy weak l∞ -solution is proved in 2-D. Finally, we performed numerical experiments with these schemes for system of Euler equations in both 1-D and 2-D, and the results showed that these schemes had high resolution ability for shocks, rarefactions and contact discontinuities. In this paper, generalized from some monotone scheme, a class of MUSCL- Type finite difference E schemes is presented. It is proved to have second order accuracy both in space and time. And applying the theory of entropy measure- valued solution, we proved the family of approximate solutions converge to the unique entropy weak l∞-solution. Based on the character in 1-D, the convergence to the unique entropy weak l∞-solution is proved in 2-D. Finally, we performed numerical experiments with these schemes for system of Euler equations in both 1-D and 2-D, and the results showed that these schemes had high resolution ability for shocks, rarefactions and contact discontinuities.