Using population synthesis, we study a double-degenerate (DD) scenario for Type Ia supernovae (SNe Ia), aiming to estimate the maximum possible contribution to the rate of SNe from this scenario and the dependence of the delay-time distribution (DTD) on it. We make an extreme assumption that all mergers of super-Chandrasekhar pairs of CO white dwarfs (WDs) and mergers of CO WDs more massive than 0.47 M⊙ with hybrid or helium WDs more massive than 0.37 M⊙ produce SNe Ia. The models are parametrized by the product of the common envelope efficiency and the parameter of binding energy of stellar envelopes, αce λ, which we vary between 0.25 and 2. The best agreement with observations is obtained for αce λ = 2. A substantial contribution to the rate of SNe Ia is provided by the pairs with a hybrid WD. The estimated Galactic rate of SNe Ia is 6.5 × 10-3 yr-1 (for the mass of the bulge and thin disc equal to 7.2 × 1010M⊙), which is comparable to the observational estimate (5.4 ± 0.12) × 10-3 yr-1. The model DTD for 1 ≤ t ≤ 8 Gyr satisfactorily fits the DTD for SNe Ia in the field galaxies (Maoz, Mannucci & Brandt). For this epoch, the model DTD is ∝t-1.64. At earlier and later epochs, our DTD has a deficit of events, as in other studies. Marginal agreement with the observational DTD is achieved even if only CO+CO WDs with M1 ≥ 0.8M⊙ and M2 ≥ 0.6M⊙ produce SNe Ia. A better agreement of observed and modelled DTD may be obtained if tidal effects are weaker than assumed and/or the metallicity of the population is much lower than solar. [ABSTRACT FROM AUTHOR]