We propose a Ge / Si graded junctionless transistor (JLT) which helps to reduce the band-to-band tunneling current in off-state for highly doped double gate junctionless transistor (DGJLT). In this paper, we show that there is large band-to-band tunneling (BTBT) current in off-state of silicon-channel and germanium-channel DGJLT, which causes increase in the off-state leakage current by several orders. With the help of band-gap engineering, we found that by using Ge / Si graded channel DGJLT off-state band-to-band tunneling current can be reduced. It is also observed that there is large deviation in the off-state leakage current with variation of drain voltage for Si and Ge body DGJLT, which reduces device stability. It is found that in Ge / Si graded DGJLT variation off-state leakage current with drain voltage is controlled. In Si and Ge , DGJLT electrons from the valence band of the channel tunnel to the conduction band of drain leaves holes which causes increased hole concentration in the channel creating parasitic 'BJT'.