  In this paper we consider a class of inflation models on the brane where the
dominant part of the inflaton scalar potential does not depend on the inflaton
field value during inflation. In particular, we consider supernatural
inflation, its hilltop version, A-term inflation, and supersymmetric (SUSY) D-
and F-term hybrid inflation on the brane. We show that the parameter space can
be broadened, the inflation scale generally can be lowered, and still possible
to have the spectral index $n_s=0.96$.
