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In this talk which is based on a joint work with Kentaro Saji given in [1], we deal with Legendrian dual surfaces in hyperbolic 3-space by using the extended Legendrian dualities between hyperbolic 3-space and one-parameter families of the pseudo-hyperspheres depending on a parameter ϕ ∈ [0, π/2] in Lorentz-Minkowski 4-space. We point out that we are interested in the case when the Legendrian dual is a spacelike curve in the dual pseudo-hypersphere depending on ϕ. Moreover, we investigate the singularities of these surfaces and the dualities of the singularities. References: [1] K. Saji, H. Yıldırım, Legendrian dual surfaces in hyperbolic 3-space, Annales Polonici Mathematici 115 (2015), no. 3, 241-261.