The electronic band structure and Fermi surface of ZrTe3 was determined by angle-resolved photoemission spectroscopy. Several bands and a large part of the Fermi surface are found to be split by 100-200 meV into two parallel dispersions. Calculations of the bulk band structure cannot reproduce this splitting even if spin-orbit interaction is taken into account. A bilayer model representing the top layers of a surface-relaxed structure without reconstruction introduces the observed splitting and reproduces most features observed in the data thus suggesting a surface relaxation of the freshly cleaved ZrTe3. The dispersion of the highly nested small electron pocket that gives rise to the charge density wave is traceable even in the low-temperature gapped state and the gap energy is determined as epsilon(g)=65+/-10 meV.