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 .