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Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investi-gated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger cntanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality de-pends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.