In the framework of the minimal supersymmetric model we examine the Z-peak constraints on the scenario of one light bottom squark (sbottom) ( approximately 2-5.5 GeV) and light gluino (approximately 12-16 GeV), which has been successfully used to explain the excess of bottom quark production in hadron collisions. Such a scenario is found to be severely constrained by the CERN LEP Z-peak observables, especially by R(b), 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 2sigma(3sigma) level, which, however, is disfavored by CERN LEP II experiments.