We report experimental results for the Kelvin-Helmholtz instability between two immiscible fluids in parallel flow in a Hele-Shaw cell. We focus our interest on the influence of the gap size between the walls on the instability characteristics. Experimental results show that the instability threshold, the critical wavelength, the phase velocity, and the spatial growth rate depend on this gap size. These results are compared to both the previous two-dimensional analysis of Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] and the three-dimensional analysis recently derived by Plouraboué and Hinch [Phys. Fluids (to be published)], showing that the agreement is still not complete especially when gap size increases.