  In the Affleck-Dine mechanism of baryogenesis, non-topological solitons
called Q-balls can be formed. In this work we study the Q-balls which decay
during the Big Bang Nucleosythesis (BBN) era. We show that such late-decaying
baryonic Q-balls with lifetime of about 10^3 s can provide a new developing
mechanism for the BBN through a rolling baryon to photon ratio \eta, which can
naturally explain the discrepancy of BBN prediction with the WMAP data on ^7Li
abundance. For the late-decaying leptonic Q-balls with lifetime of about 10^6
s, we find that their decay product, gravitino, can serve as a dark matter
candidate without overclosing the universe and, at the same time, can give an
explanation of the approximate equality of dark and baryon matter densities.
