Whether the algorithm noise can be effectively wiped off decides the success or loss of the power analysis attack. This paper offers a new differential power analysis attack algorithm, which is based on the consumed power differences between two neighboring clock cycles of liner feedback shift register. This new attack algorithm radically wipes off the effect of cipher algorithm noise in the process of attack. Because this algorithm randomly chooses initialization vectors, the attackers can easily extend the algorithm to other stream ciphers that have similar structures. In order to further validate the algorithms availability, simulative attacks on DECIM are carried on with the method of software simulation. And the result shows that this algorithm can effectively reduce the complexity of the exhaustive search on LFSR.