  Theories of gravity for which gravitons can be treated as massive particles
have presently been studied as realistic modifications of General Relativity,
and can be tested with cosmological observations. In this work, we study the
ability of a recently proposed theory with massive gravitons, the so-called
Visser theory, to explain the measurements of luminosity distance from the
Union2 compilation, the most recent Type-Ia Supernovae (SNe Ia) dataset,
adopting the current ratio of the total density of non-relativistic matter to
the critical density ($\Omega_m$) as a free parameter. We also combine the SNe
Ia data with constraints from Baryon Acoustic Oscillations (BAO) and CMB
measurements. We find that, for the allowed interval of values for $\Omega_m$,
a model based on Visser's theory can produce an accelerated expansion period
without any dark energy component, but the combined analysis (SNe Ia + BAO +
CMB) shows that the model is disfavored when compared with $\Lambda$CDM model.
