  We study inflation driven by the tachyon field in the holographic braneworld
by assuming the second slow-roll parameter $\eta$ is constant. The parameter
$\eta$ can be either defined by the tachyon scalar field and the Hubble
parameter or by the Hubble parameter only. By assuming a constant $\eta$, we
derive and numerically solve a differential equation for the Hubble expansion
rate. We calculate numerically the scalar spectral index and the
tensor-to-scalar ratio. We confront the results with the observational data and
find some constraints on the free model parameters. The swampland conjectures
are discussed in the context of the constant-roll inflation, with some accent
on the holographic model.
