In adaptive radiation, a single species evolves into many ecologically diverse species in short term. It has been suggested that some adaptive radiations might have been triggered by inter-specific hybridization. Hybridization assembles genes from different parental species and can increase phenotypic variation in offspring individuals, which could facilitate their adaptation to diverse ecological niches. At the same time, adaptive radiation requires reproductive isolation to be developed between ecologically-diversified daughter species. Evolution of reproductive isolation is known to develop naturally if "magic traits" causing ecological divergence contribute also to assortative mating. Here, we explore conditions in which the co-action of hybridization and magic trait evolution causes adaptive radiation. We perform computer simulations of adaptive radiations that are initiated by secondly contact of three hybridizing species. We show that an adaptive radiation occurs most frequently when magic traits are involved in moderate levels of assortative mating. Weak assortative mating does not cause reproductive isolation, while strong assortative mating prevents ecological diversification by forbidding hybridization. Our results highlight important roles of hybridization and magic traits in causing adaptive radiation.