The present work develops a strain rate-dependent cohesive zone model and related finite element model to analyze speed-dependent dynamic fracture of pipeline steels observed in recent drop-weight tear tests. Different than most of existing cohesive zone models, the traction-separation law of the present model considers the rate of separation in the cohesive zone, and a rate-dependent elastic-viscoplastic constitutive model is employed for the bulk material. The speed-dependences of CTOA and energy dissipation observed experimentally are reproduced in our simulations for moderate steady-state crack speed (up to 150 m/s). The present model gives detailed stress-strain fields surrounding the moving crack tip, which offer plausible explanation why the rate-effects in the bulk material and the cohesive zone could be largely responsible for all observed speed-dependent dynamic fracture phenomena of pipeline steels.