Vertical-axis wind turbines have the potential to increase the share of primary energy from wind. The development of vertical-axis wind turbines for large-scale application has been limited by their self-starting capabilities and the occurrence of dynamic stall on the blades. In the present work, we investigate the asymmetry in the development of dynamic stall between the upwind and downwind half of one turbine blade rotation. Particle image velocimetry and load measurements were performed on a scaled-down H-type Darrieus wind turbine that was placed in a water channel. The wind turbine was operated at a chord-based Reynolds number Re = 50 000 and tip-speed ratio lambda = 1.5. The total force coefficient was found to peak at 4 in the upwind half and 1.5 in the downwind half. The formation of a coherent large-scale dynamic stall was evidenced in the upwind half of a turbine rotation and no coherent flow structures could be identified in the downwind half. Three main reasons were identified to explain the asymmetry between the upwind and downwind halves of the turbine rotation: (i) blade kinematics allow for sufficient time for vortex formation in the upwind half, but not in the downwind half, (ii) the shear layer is initially attached during upwind and heavily separated during downwind, and (iii) the vortex-induced velocity is below 5 % of the characteristic blade velocity at the beginning of the upwind and above 60% at the beginning of the downwind.