The goal of this talk is to construct a p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. Glenn Stevens proved that there is a $\Lambda$-adic lifting of this map to the Hida family of ordinary cusp forms of integral weight via the cohomological description of the Shintani correspondence, and consequently constructed a $\Lambda$-adic modular eigenform of half-integral weight. The natural thing to do is generalize his result to the non-ordinary case, i.e. Coleman's p-adic analytic family of overconvergent cusp forms of finite slope. For this we will use a slope h decomposition of compact supported cohomology with values in overconvergent distribution (overconvergent modular symbol), which can be interpreted as a cohomological description of Coleman's p-adic family, and define the p-adic Hecke algebra for the slope h part of this cohomology. Then we follow the idea of Stevens in the ordinary case. This construction implies that we found a local rigid analytic map from Coleman-Mazur integral weight Eigencurve to half-integral weight eigencurve. The important feature of overconvergent Shintani lifting is that it is purely cohomological and algebraic, which depends only on the arithmetic of integral indefinite binary quadratic forms, so that we can describe Hecke operators explicitly on q-expansion of universal overconvergent half-integral weight modular forms using the Hecke action on overconvergent modular symbol.