Logistic map and its variable substitution model are the well-known period doubling bifurcation and chaos model,the control and anti-control of their bifurcation behavior are very important work.Bifurcation properties of a system can be modied by various feedback controllers.This paper discusses the anti-control of period doubling bifurcations for the one-dimensional variable substitution model of Logistic map.Using feedback control we can arbitrarily change the period-2 point,that is,create the period-2 bifurcation point in a bigger region.The control gains of anti-controlling period doubling bifurcation may be determined by the analytic method or the numerical iteration technique,.New research methods and results of anti-controlling bifurcation will appear under pursuing further in this promising direction of new field.