Context. Particle-accelerating colliding-wind binaries (PACWBs) are systems that are formed by two massive and hot stars and produce nonthermal radiation. The key elements of these systems are fast winds and the shocks that they create when they collide. Binaries with nonaccreting young pulsars have also been detected as nonthermal emitters, again as a consequence of the wind-wind interaction. Black holes might produce nonthermal radiation by this mechanism if they accrete at super-Eddington rates. In such cases, the disk is expected to launch a radiation-driven wind, and if this wind has an equatorial component, it can collide with the companion star yielding a PACWB. These systems are supercritical colliding wind binaries. Aims. We aim to characterize the particle acceleration and nonthermal radiation produced by the collision of winds in binary systems composed of a superaccreting black hole and an early-type star. Methods. We estimated the terminal velocity of the disk-driven wind by calculating the spatial distribution of the radiation fields and their effect on disk particles. We then found the location of the wind collision region and calculated the timescales of energy gain and losses of relativistic particles undergoing diffusive particle acceleration. With this information, we were able to compute the associated spectral energy distribution of the radiation. We calculated a number of specific models with different parameters to explore this scenario. Results. We find that the interaction of winds can produce nonthermal emission from radio up to tens of GeV, with luminosities in the range of ∼ 10 33 -10 35 erg s −1 , which for the most part are contributed by electron synchrotron and inverse Compton radiation. Conclusions. We conclude that supercritical colliding wind binaries, such as some ultraluminous X-ray sources and some Galactic X-ray binaries, are capable of accelerating cosmic rays and producing nonthermal electromagnetic emission from radio to γ-rays, in addition to the thermal components.