Serpent is one of the five AES finalist. In 2001, Biham, Dunkelman and Keller present a differential cryptanalysis of Serpent up to 8 rounds with 256-key bits by using $2^{14}$ 6-round differential characteristics with probability $2^{-93}$. In this paper we present a new 6-round differential characteristic $\Omega_A$ with the same probability $2^{-93}$. By changing the input differences of $\Omega_A$, we get a characteristic $\Omega_B$ with probability $2^{-95}$. We give an improved differential attack on 8-round Serpent with 256-bit keys by using $2^{19.62}$ 6-round characteristics with probability $2^{-95}$. Similarly, we present an improved differential attack on 8-round Serpent with 256-bit keys by using $2^{25.24}$ 6-round characteristics with probability $2^{-97}$.