Why don't Jews believe in afterlife?

Hell is not mentioned in any part of the Jewish Bible. It is only in the New Testament where Hell is first mentioned, along with the concept of eternal damnation. As it has no part or history in Jewish tradition, it is not believed in.

The question is mistaken. Does Judaism believe in the existence of hell? The name and details are probably different than in other religions, but the short answer is yes. "And they shall go forth, and look upon the carcasses of the men that have rebelled against Me; for their worm shall not die, neither shall their fire be quenched" (Isaiah 66:24). One of the central beliefs of Judaism, as codified by Rambam (Maimonides, 1135-1204), is that the soul continues to exist after death and is treated in accordance with the person's actions while he/she was alive. All outstanding accounts are settled after this life. Some cases illustrate this point, since this entire world wouldn't be enough to reward a Moses or punish a Hitler.
The afterlife is discussed at length in the Talmud, though the exact nature of the rewards and punishments is generally not given since it would be like describing the colors of a sunrise to someone who was blind from birth. See for example the Talmud, Rosh Hashanah 17a, for a few details.
It is important to note that Judaism is a rare case in that it does not condemn non-adherents to eternal damnation. Worthy non-Jews are able to merit the rewards in the afterlife without conversion.
Another important point is the efficacy of repentance, which can change one's spiritual "balance" relatively easily. See for example Deuteronomy 30:1-10 for one of the Tanakh's many passages on this topic.