The dynamic behavior of journal bearing lubricated by non-Newtonian fluid (conforms to the Carreau model) during start-up is investigated. A mixed lubrication model consisting of a GT (Greenwood-Tripp) contact equation and transient modified average Reynolds equation is proposed. The transient modified average Reynolds equation is established with the average flow method. The effect of non-Newtonian lubricant, surface roughness, external load, relative clearance, and accelerating time on the dynamic behavior of journal bearings during start-up is analyzed. The results show that increasing the relaxation time, external load, and relative clearance, as well as decreasing the power-law exponent, composite root-mean-square roughness and accelerating time can reduce the contact time and facilitate the rapid formation of hydrodynamic lubrication during start-up.