  In the present paper, we aim to generalize the constant-roll inflation in the
non-canonical set-up, particularly in the context of scalar Dirac-Born-Infeld
(DBI) theory which has emerged to be prospective candidate for describing
inflation in the realm of string theory and in general permits time dependent
speed of sound. Assuming the simplest case, when the speed of sound of scalar
fluctuations is constant but different from unity, we obtain exact inflationary
solutions and corresponding solutions of warp factors under constant-roll
conditions. In this scenario, the inflationary solution is found to be an
attractor. The power spectra of curvature fluctuations is analysed in the DBI
regime and finally an estimation for predicting the observational bound on the
DBI constant roll parameter is performed by using the the values of scalar
spectral index and speed of sound provided by Planck and WMAP data.
