In recent years, atmospheric-pressure plasma jets (APPJs) have emerged as valuable tools in many application areas, including material modification, environmental remediation and biomedicine. Understanding the discharge characteristics of these plasma jets under various operating conditions is crucial for optimizing process outcomes. This paper presents a two-dimensional fluid model for numerical simulation to study the variation in electron density within an atmospheric-pressure helium plasma jet under different operating conditions. The investigated parameters include helium gas flow rate, voltage amplitude, needle-to-ring discharge gap, and relative permittivity of the dielectric tube. The results reveal that the peak electric field and electron density initially occur at the wall of the dielectric tube and subsequently shift towards the head of the propagating jet. Gas flow rate has minimal impact on the electron density throughout the plasma jet, whereas increasing the needle-to-ring discharge gap significantly decreases the average electron density within the jet. In addition, an increase in the voltage amplitude and the relative permittivity of the dielectric tube enhances the electric field within the discharge space, thereby increasing the electron density in the plasma jet. These findings underscore the importance of understanding the correlation between electron density and operating conditions to precisely control plasma jets and enhance material treatment effectiveness for specific applications.