In the case of the journal-bearing system under a mixed or boundary lubrication regime, the deformation of the bearing, the flow of the lubricating medium, and the contact of the asperities should be taken into account. The lubrication problem at the journal-shaft interface is a complicated fluid–solid coupling problem. In this study, a new approach is proposed to analyze the dynamic fluid–solid coupling problem of journal bearings. The dynamic fluid–solid coupling problem is solved by the presented non-linear hybrid conjugate gradient method, which is based on the principle of pressure balance in the lubrication zone. One transient mixed lubrication model was developed to analyze the journal-bearing performance by considering the effects of skewness and kurtosis and the mass-conserving cavitation. According to the simulated results from the journal-bearing systems under the start-up condition, it can be found that the bearing performance is sensitive to the value of skewness or kurtosis and the degree of misalignment. Within a certain range, these cases with more negative skewness or lower kurtosis are conducive to decreasing friction loss and lift-off time. The developed model can be effectively used to track the performance of journal bearings.