To describe a massive particle with fixed, but arbitrary, spin on d = 4 anti-de Sitter space M4, we propose the point particle model with configuration space M6 = M4 × S2, where the sphere S2 corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase space counterparts of the second and fourth order Casimir operators for so(3,2). We prove that the requirement of energy to have a global positive minimum Eo over the configuration space is equivalent to the relation Eo > s, s being the particle's spin, which presents the classical counterpart of the quantum massive condition. States with minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on d-dimensional anti-de Sitter space Md, with M2(d-1) = Md × S(d-2) the corresponding configuration space.