This paper presents a complete dispersion analysis of a tunable graphene-based Fabry-Perot cavity in the THz range. The structure consists of a grounded dielectric slab covered by a graphene partially-reflecting sheet whose surface conductivity can easily be tuned by applying an electrostatic bias. Complex TE and TM modes in bound regimes (surface waves including plasmon polaritons) as well as in radiative regimes (leaky waves) are taken into account. The analysis reveals a very interesting behavior of the fundamental leaky modes for practical values of the bias. In particular, we illustrate how a graphene-based FPC can attractively be used as a reconfigurable leaky-wave radiator operating in the THz range.