Very high energy (VHE) emission is usually interpreted in the synchrotron self-Compton scenario and expected from the low-redshift and high-luminosity gamma-ray bursts (GRBs), such as GRB 180720B and GRB 190114C. Recently, the H.E.S.S. telescopes reported VHE emission from one of the closest bursts, GRB 190829A, which was associated with the supernova 2019oyw. In this paper, we present a temporal and spectral analysis from optical bands to the Fermi-LAT energy range over multiple observational periods beginning after the trigger time and extending for almost 3 months. We show that the X-ray and optical observations are consistent with synchrotron forward-shock emission evolving between the characteristic and cooling spectral breaks during the early and late afterglow in a uniform-density medium. Modeling the light curves together with the spectral energy distribution, we show that the outflow expanded with an initial bulk Lorentz factor of Γ ∼ 30, which is high for low-luminosity GRBs and low for high-luminosity GRBs. The values of the initial bulk Lorentz factor and the isotropic-equivalent energy suggest that GRB 190829A is an intermediate-luminosity burst; consequently, it becomes the first burst of this class to be detected in the VHE gamma-ray band by an imaging atmospheric Cherenkov telescope and, in turn, the first event to not be simultaneously observed by the Fermi-LAT instrument. Analyzing the intermediateluminosity bursts with z 0.2, such as GRB 130702A, we show that bursts with intermediate luminosities are potential candidates to be detected in VHEs.