In this paper, a mixed lubrication model is presented to analyze the tribological behavior of the textured journal bearings operating from mixed to hydrodynamic lubrication regimes. In particular, the effects of fluid piezoviscosity and the non-Newtonian fluid behavior are also considered. The presented model solves the hydrodynamic lubrication problem by a mass-conserving formation of the Reynolds equation. Whereas, the metal-metal contact is considered by using the Greenwood and Tripp contact model, which is linked with the hydrodynamic model based on the concept of Johnson's load sharing. As a result, the performance of the textured journal bearing system under different lubrication regimes, including boundary lubrication regime, mixed hydrodynamic lubrication regime and hydrodynamic lubrication regime can be evaluated. Using the journal bearing systems operated under the start-up condition as examples, prediction demonstrates the influences of texture distributions on friction and wear. Moreover, the effect of non-Newtonian lubricants is also performed.