  We provide a cosmological test of modified gravity with two tensorial degrees
of freedom and no extra propagating scalar mode. The theory of gravity we
consider admits a cosmological model that is indistinguishable from the
$\Lambda$CDM model at the level of the background evolution. The model has a
single modified-gravity parameter $\beta$, the effect of which can be seen in
linear perturbations, though no extra scalar mode is propagating. Using the
Boltzmann code modified to incorporate the present model, we derive the
constraints $-0.047 < \beta < -0.028$ at 68$\%$ confidence from Planck CMB
data. Since our modified gravity model can hardly be constrained by the Solar
System tests and gravitational-wave propagation, our result offers the first
observational test on the model.
