Using the constant-roll approach, DBI inflationary scenario will be studied and it is sought to compare the result with observational data. By considering the cosmological perturbations of the model, it is realized that some extra terms appear in the amplitude of scalar perturbations which indicates that there should be a modified version of the scalar spectral index and tensor-to-scalar ratio. To compare the model with observational data, some specific functions of the scalar field are assumed for the f (φ) function. For power-law and exponential functions, a constant slow-roll parameter ϵ is obtained which produces difficulties for the graceful exit from inflation. Then, a product of linear and exponential function, and also a hyperbolic function of the scalar field are selected for f (φ), that results in a ϵ(φ) with an end for the accelerated expansion phase. Considering the scalar spectral index, the amplitude of scalar perturbations and tensor-to-scalar ratio shows that for some values of the constant η = β there could be a good consistency between the model prediction and observational data. Then, based on the form of the equation of motion of the scalar field a new interesting definition for the second slow-roll parameter is present and the behavior of the perturbation parameters is reconsidered. The results come to a good agreement with observational data. Finally, the attractor behavior of these two last cases is investigated and it is determined that this feature could be satisfied.
