  We investigate inflation and its scalar perturbation driven by a massive
scalar field in the unimodular theory of gravity. We introduce a parameter
$\xi$ with which the theory is invariant under general unimodular coordinate
transformations. When the unimodular parameter is $\xi=6$, the classical
picture of inflation is reproduced in the unimodular theory because it recovers
the background equations of the standard theory of general relativity. We show
that for $\xi=6$, the theory is equivalent to the standard theory of general
relativity at the perturbation level. Unimodular gravity constrains the gauge
degree of freedom in the scalar perturbation, but the perturbation equations
are similar to those in general relativity. For $\xi \neq 6$, we derive the
power spectrum and the spectral index, and obtain the unimodular correction to
the tensor-to-scalar ratio. Depending on the value of $\xi$, the correction can
either raise or lower the value of the tensor-to-scalar ratio.
