We derived constraints on cosmological parameters using weak lensing peak statistics measured on the similar to aEuro parts per thousand 130 deg(2) of the Canada-France-Hawaii Telescope Stripe 82 Survey. This analysis demonstrates the feasibility of using peak statistics in cosmological studies. For our measurements, we considered peaks with signal-to-noise ratio in the range of nu = [3, 6]. For a flat I > cold dark matter model with only (Omega(m), sigma(8)) as free parameters, we constrained the parameters of the following relation I (8) pound = sigma(8)(Omega(m)/0.27)(alpha) to be I (8) pound = 0.82 +/- 0.03 and alpha = 0.43 +/- 0.02. The alpha value found is considerably smaller than the one measured in two-point and three-point cosmic shear correlation analyses, showing a significant complement of peak statistics to standard weak lensing cosmological studies. The derived constraints on (Omega(m), sigma(8)) are fully consistent with the ones from either WMAP9 or Planck. From the weak lensing peak abundances alone, we obtained marginalized mean values of tex-math id="TM0002" notation="LaTeX"$\Omega _{\rm m}=0.38<^>{+0.27}_{-0.24}$/tex-math and sigma(8) = 0.81 +/- 0.26. Finally, we also explored the potential of using weak lensing peak statistics to constrain the mass-concentration relation of dark matter haloes simultaneously with cosmological parameters.