Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bells theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardys paradox is an important all-versus-nothing proof and is considered as the simplest form of Bells theorem. In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardys paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit two-setting case, and the corresponding successful probability is about four times larger than the original one, thus providing a more friendly test for experiment. We also find that GHZ paradox can be viewed as a perfect Hardy-type paradox. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.
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