Abstract: Voltage is an important parameter for characterizing the operating status of power lines, and achieving flexible and accurate voltage measurements is crucial for ensuring the stable operation of the power system. Traditional contact-based voltage measurement methods have drawbacks such as large size of voltage transformers, electromagnetic resonance and high-frequency oscillations, and the need for power outage during installation, making it inconvenient for massive measurements. In contrast, non-contact measurement, which does not require direct contact with the conductors, offers improved safety and convenience, and is considered as the future direction for voltage measurement. This paper presents a non-contact voltage measurement method for transmission lines based on an array of electric field sensors. To address the issue of unknown conductor position information, the method employs an electric field sensor array arranged perpendicularly to the direction of the conductors. By solving the equations involving unknown conductor information, a coefficient matrix is constructed to estimate the instantaneous values of conductor voltages. The influence of electric field sensors on the measurement is analyzed. Finally, a simulation verification of instantaneous voltage values at the 10 kV voltage level is conducted, demonstrating a maximum measurement error of 2.219%.