Conformal-projective geometry of statistical manifolds, a natural generalization of conformal geometry of Riemannian manifolds, is studied in this paper. In particular, several fundamental results in the geometry are given: a geometric criterion for two statistical manifolds to be conformally-projectively equivalent; conditions for a statistical manifold to be conformally-projectively flat; properties of umbilical hypersurfaces of a conformally-projectively flat statistical manifold.