A model of continuous dephasing for one-dimensional mesoscopic conductors is proposed. The model is based on Buttiker's fictitious-probe model which is extended by attaching an infinite number of probes uniformly to various points on the conductor. The associated scattering problem is then solved. When the continuum limit is taken, it becomes possible to describe the dephasing as taking place everywhere. The dephasing rate enters into the model as an adjustable parameter. The effect of dephasing on the conductance for a double-barrier system is also studied numerically. (C) 2011 Elsevier B.V. All rights reserved.