Here is a list of verbs that start with CUR.
curb, curbing, curdling, cure, cured
curing, curl, curled, curling, curse
cursed, cursing, curtail, curtailed, curtseyed
curved, curving
Hope you enjoy this page of verbs that start with cur and the rest of this verb list site as well.
Did I miss any verbs? Visitors can make this a more useful online resource by listing more verbs in the comments.