It is shown that surface domain structure arises in magnetic nanotube with uniaxial anisotropy if surface anisotropy constant is negative and sufficiently high in absolute value. The surface magnetic anisotropy affects also the structure and dynamics of a head-to-head domain wall propagating along the nanotube axis in applied magnetic field. The hopping mode is observed for stationary movement of a head-to-head domain wall. The average speed of the domain wall in the hopping mode is found to be several times less than the stationary velocity of the wall in the absence of surface anisotropy. This effect is important for various applications where fast propagation of the domain wall along the sample is essential. (C) 2016 Elsevier B.V. All rights reserved.