Concerning the failure problem of fault attack on elliptic curve scalar multiplication algorithm, an improved algorithm of differential fault attack was proposed. The nonzero assumption was eliminated, and an authentication mechanism was imported against the failure threat of "fault detection". Using the elliptic curve provided by SM2 algorithm, the binary scalar multiplication algorithm, binary Non-Adjacent Form (NAF) scalar multiplication algorithm and Montgomery scalar multiplication algorithm were successfully attacked with software simulation. The 256-bit private key was restored in three hours. The attacking process of binary NAF scalar multiplication algorithm was optimized, so the attack time was reduced to one fifth of the original one. The experimental results show that the proposed algorithm can improve the effectiveness of the attack.