We consider a simple supersymmetric grand unified model which naturally solves the strong CP and μ problems via a Peccei-Quinn symmetry and leads to the standard realization of hybrid inflation. We show that the Peccei-Quinn field of this model can act as a curvaton. In contrast to the standard curvaton hypothesis, both the inflaton and the curvaton contribute to the total curvature perturbation. The model predicts the existence of an isocurvature perturbation, too, which has mixed correlation with the adiabatic one. The cold dark matter of the Universe is mostly constituted by axions, which are produced at the QCD phase transition, plus a small amount of lightest sparticles. The predictions of the model are confronted with the first-year Wilkinson microwave anisotropy probe and other cosmic microwave background radiation data. We analyze in detail two representative choices of parameters for our model and derive bounds on the curvaton contribution to the adiabatic perturbation. We find that, for the choice which provides the best fitting of the data, the curvaton contribution to the amplitude of the adiabatic perturbation must be smaller than about 67% and the amplitude of the partial curvature perturbation from the curvaton smaller than 43.2×10−5 (both at 95% confidence level). The best-fit power spectra are dominated by the adiabatic part of the inflaton contribution. We use Bayesian model comparison to show that this choice of parameters is disfavored with respect to the pure inflaton scale-invariant case with odds of about 50 to 1. For the second choice of parameters examined, the adiabatic mode is dominated by the curvaton, but this choice is strongly disfavored relative to the pure inflaton scale-invariant case (with odds of about 107 to 1). We conclude that in the present framework the perturbations must be dominated by the adiabatic component from the inflaton.