Installing a flow conditioner is an important method for rectifying irregular and unstable flow to stable flow state within a short flow distance in fluid transportation and control industrial applications. However, classical flow conditioners (such as Laws and Zanker flow conditioners in ISO 5167) with parallel pipeline axial orifices ineffectively rectify the distinct eccentric jet flow caused by valve regulation. The convergence flow conditioner with convergent orifices was innovatively designed for rectifying the eccentric jet flow caused by a ball valve in this study. Three convergent orifice angles (8°, 10°, and 12°) defined as angles between orifice and pipeline axes were considered to compare their effect on eccentric jet flow rectification as well as with the classical Laws flow conditioner (characterized by the convergent orifice angle of 0°) under different valve openings with an experimental setup for monitoring downstream pressures that develop along the pipeline and corresponding numerical simulation used. Pressure loss and throttling effect of installing convergence flow conditioners downstream the ball valve was assessed. Analysis of distributions of the pressure, velocity, and streamline for convergent flow conditioners showed that the flow conditioner with a large convergent orifice angle can effectively improve violent eccentric jet flows, especially under a small valve opening. The axial velocity on various downstream cross sections was extracted to evaluate the velocity uniformity. A dimensionless parameter of velocity eccentric ratio was used to quantify the rectification effect of eccentric jet flow evolving in the downstream pipeline. Results showed that a short pipeline length is needed to obtain additional symmetry and uniform flow field downstream of the flow conditioner with a high convergent orifice angle, that is, the convergence flow conditioner with a high convergent orifice angle demonstrated a strong effect of flow rectification on the valve-induced eccentric jet flow. This work can help understand characteristics of flow rectification on valve-induced eccentric jet flow in scientific research, and provide guidance for the flow conditioner design in fluid engineering.