The energy dependence of the photon-proton total cross section, sigma(gamma p)(tot), was determined from e(+) p scattering data collected with the ZEUS detector at HERA at three values of the center-of-mass energy, W, of the gamma p system in the range 194 < W < 296 GeV. This is the first determination of the W dependence of sigma(gamma p)(tot) from a single experiment at high W. Parameterizing sigma(gamma p)(tot) alpha W-2 epsilon, epsilon = 0.111 +/- 0.009 (stat.) +/- 0.036 (syst.) was obtained. (c) 2011 Elsevier B.V. All rights reserved.