ABSTRACT We derive for the first time the dust mass function (DMF) in a wide redshift range, from z ∼ 0.2 up to z ∼ 2.5. In order to trace the dust emission, we start from a far-IR (160-μm) Herschel selected catalogue in the COSMOS field. We estimate the dust masses by fitting the far-IR data (λrest$\,\, \buildrel\gt \over ∼ \,\,$50 μm) with a modified black body function and we present a detailed analysis to take into account the incompleteness in dust masses from a far-IR perspective. By parametrizing the observed DMF with a Schechter function in the redshift range 0.1 < z ≤ 0.25, where we are able to sample faint dust masses, we measure a steep slope (α ∼1.48), as found by the majority of works in the Local Universe. We detect a strong dust mass evolution, with $M_{\rm d}^{⋆ }$ at z ∼ 2.5 almost 1 dex larger than in the local Universe, combined with a decrease in their number density. Integrating our DMFs, we estimate the dust mass density (DMD), finding a broad peak at z ∼ 1, with a decrease by a factor of ∼ 3 towards z ∼ 0 and z ∼ 2.5. In general, the trend found for the DMD mostly agrees with the derivation of Driver et al., another DMD determination based also on far-IR detections, and with other measures based on indirect tracers.