In this paper, we introduce and study the notions of Hom-reflection space and Hom-symmetric space. We provide some examples of Hom-reflection spaces (resp. Hom-symmetric spaces) by using ordinary reflection (resp. symmetric) spaces. Also, we associate a Hom-reflection (resp. Hom-symmetric) space to a Hom-Lie group. Finally, we provide some properties of a Hom-Jordan algebra and show that there is a relationship between Hom-Jordan algebras and Hom-symmetric spaces.
