In the framework of minimal supersymmetric model we examine the Z-peak
constraints on the scenario of one light sbottom (2--5.5 GeV) and
light gluino (12--16 GeV), which has been successfully used to explain
the excess of bottom quark production in hadron collision. Such a
scenario is found to be severely constrained by LEP Z-peak
observables, especially by Rb, due to the large effect of
gluino-sbottom loops. To account for the R_b data in this scenario,
the other mass eigenstate of sbottom, i.e., the heavier one, must be
lighter than 125 (195) GeV at 2-sigma (3-sigma ) level, which should
have been produced in association with the lighter one at LEP II and
will probobaly be within the reach of Tevatron Run 2.