The present work analyzes the cyclic variability in spark ignition engines fuelled by different gasoline-hydrogen blends by means of quasi-dimensional computer simulations. The cyclic variability is a well-known phenomenon in this kind of engines, especially when operating at lean conditions. It can affect engine stability and efficiency to a great extent. Among its main causes is the development of turbulent combustion in each cycle, which is associated with turbulent flow during admission. On the other hand, hydrogen is a fuel known by its elevated laminar flame speed, which is in principle interesting to increase the rate of combustion, and so decrease cyclic variability effects. Our group has developed a quasi-dimensional numerical simulation that incorporates cycle-to-cycle variability. In the present work, the effect of hydrogen addition is considered in the model. Wrinkled flame effects are taken into account by introducing a linear factor dependent on the amount of hydrogen in the fuel, affecting the flame area development. The model is validated by direct comparison with experimental results. Studying the coefficient of variation of power output time series, it is concluded that for lean mixtures, when the percentage of hydrogen increases, the cyclic variability decreases up to a minimum value, which depends on the fuel-air equivalence ratio. Minimum values of cyclic variability amplitude are observed at fuel ratios near 0.9 and 70% percentage of hydrogen in fuel by volume.