Let X subset of P-r be a scroll of codimension e and degree d over a smooth projective curve of genus g. The purpose of this paper is to prove a linear Castelnuovo-Mumford regularity bound that reg(X) <= d - e +1+ g(e - 1). This bound works over an algebraically closed field of arbitrary characteristic. (C) 2017 Elsevier Inc. All rights reserved.