The Trivium Stream cipher is one of the lightweight synchronous stream ciphers that won the eSTREAM project in Europe,which is a simplified version of the Trivium stream cipher for RIFD systems.The designers believe that the Enhanced-Bivium stream cipher algorithm is more secure than the Trivium stream cipher algorithm with the same number of initialization rounds.This article proposes a new cube attack method by introducing an algebraic degree evaluation method in the offline preprocessing stage and a cube attack based on monomial prediction in the online computing stage.With the new method,we can reduce the time complexity of the cube attack on the Enhanced-Bivium stream cipher with 464 initial rounds from 2 55 to 2 50.3.At the same time,the number of initialization rounds of successful key recovery attack can be increased from 464 to 601 with the improved cube attack method,and the time complexity is 277 8.Also with the same time complexity,the initial rounds number of successful cube attacks on Trivium stream ciphers can be increased from 799 to 840,which proves that Enhanced-Bivium stream ciphers have better resistance to cube attack than the Trivium stream cipher.