We investigate the spectral evolution of white dwarfs by considering the effects of hydrogen mass in the atmosphere and convective overshooting above the convection zone .
Our numerical results show that white dwarfs with M _ { H } \sim 10 ^ { -16 } ~ { } M _ { \odot } show DA spectral type between 46 , 000 \lesssim T _ { eff } \lesssim 26 , 000 ~ { } { K } and DO or DB spectral type may appears on either side of this temperature range .
White dwarfs with M _ { H } \sim 10 ^ { -15 } ~ { } M _ { \odot } appear as DA stars until they cool to T _ { eff } \sim 31 , 000 ~ { } { K } , from then on they will evolve into DB white dwarfs as a result of convective mixing .
If M _ { H } in the white dwarfs more than 10 ^ { -14 } ~ { } M _ { \odot } , the convective mixing will not occur when T _ { eff } > 20 , 000 ~ { } { K } , thus these white dwarfs always appear as DA stars .
White dwarfs within the temperature range 46 , 000 \lesssim T _ { eff } \lesssim 31 , 000 ~ { } { K } always show DA spectral type , which coincides with the DB gap .
We notice the importance of the convective overshooting and suggest that the overshooting length should be proportional to the thickness of the convection zone to better fit the observations .