In order to realize the effective control of welding quality, the influence of the process parameters on the composite arc voltage in the new laser–plasma arc coaxial hybrid welding of titanium alloy was investigated. An arc electrical characteristic acquisition system was adopted to collect the arc electrical signals in the process of hybrid welding, and the multiple linear regression method was utilized to construct a regression model between the process parameters and the arc voltage, so as to deeply analyze the influence rules of hybrid welding process parameters, such as nozzle height, laser power, and plasma current, on the arc voltage. The results showed that under the conditions set in this experiment, the plasma voltage in the hybrid welding fluctuated dynamically within the range of 18–36 V. Moreover, as the nozzle height, current value, and laser power gradually increased, the arc voltage showed an upward trend. Through the quantitative evaluation of the regression model, the influence of the nozzle height on the arc voltage was the most prominent, followed by the plasma current, and the laser power had the least influence. By observing the changes in the arc morphology, the accuracy of the regression model in judging the weights of the influencing factors was verified. This provided experimental evidence and theoretical basis for further optimizing the welding process.