  The beta function formalism is being used to study the constant-roll
inflation in the k-essence model. Assuming the second slow-roll parameter as a
constant leads to a first-order differential equation for $\beta$-function
which is much easier to solve and find a solution than the second (non-linear)
order equation that we have in corresponding standard constant-roll inflation.
Many cosmological models are known as a subclass of k-essence, so we will try
to consider the model as general as possible. It is determined that the second
slow-roll parameter should be positive to produce a small value for the first
slow-roll parameter. The scenario is considered for three well-known
cosmological models, and it is clarified that for the non-canonical and tachyon
model, the scalar spectral index never reaches the observational range, however
for the DBI model, we could arrive at a result consistent with observational
data.
