The beta-function formalism is being used to study the constant-roll inflation in k-essence models. Assuming the second slow-roll parameter as a constant leads to a first-order differential equation for -function which much easier to solve and find a solution than the second (non-linear) order equation that we have in the 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 as a result consistent with the observational data.
