In flow measurement and control industrial application, installing a flow conditioner is an effective way to rectify irregular and unstable flow to stable flow state within a short flow distance. To effectively rectify the eccentric jet flow caused by valve regulation in pipeline, the convergence flow conditioner with convergent orifice angles has been innovatively designed and investigated. However, the effect of structural parameters (such as flow conditioner thickness and flow area) on improving unstable eccentric jet flow rectification was still not elaborated. Thus, the effect of structural parameters of the convergence flow conditioner on rectifying eccentric jet flow was examined in this paper. The structural parameters of the flow conditioner thickness and the flow area were considered under the fixed convergence angle of 12°. The experimental system of monitoring pressures upstream and downstream of the convergence flow conditioner along the pipeline was developed and corresponding numerical simulation was employed. The flow coefficient and resistance coefficient of a convergence flow conditioner under various valve openings were accessed, and monitored pressures along the pipeline were also discussed for numerical simulation verification. The velocity and streamline distributions downstream the convergence flow conditioners were comparatively analyzed. In addition, the axial velocities on various downstream cross-sections were extracted to evaluate the velocity uniformity. A dimensionless parameter of velocity deviation ratio was introduced to quantify the rectification effect of eccentric jet flow evolving in the downstream pipeline. Results showed that the convergence flow conditioner with the thickness of 6 mm and the flow area of 50% owned a better effect on rectifying the valve-induced eccentric jet flow, that is, a shorter flow length was required for changing the valve-induced eccentric unstable flow to uniform stable flow by installing a convergence flow conditioner with above structural parameters.