In this paper we study the zeta functions associated to the minimal spherical principal series of representations for a class of reductive p-adic symmetric spaces, which are realized as open orbits of some prehomogeneous spaces. These symmetric spaces have been studied in the paper arXiv: 2003.05764. We prove that the zeta functions satisfy a functional equation which is given explicitly (see Theorem 4.3.9 and Theorem 4.4.5). Moreover, for a subclass of these spaces, we define L-functions and epsilon-factors associated to the representations.