Roll-to-roll ultraviolet (R2R-UV) imprinting is a low-cost and high-throughput method that includes the manufacturing of large-area functional films. However, the quality of the final product is obstructed by the bubble entrapment during the imprinting process. In this study, a multi-phase volume of fluid (VOF) numerical model was used to remove bubble entrapment during the R2R imprinting process, which covered all parameters. This new modified numerical model with open-channel boundary conditions was based on the single zone that contains the direct contact of UV resin with the imprinting mold during the filling process. In addition, this model simulated the UV resin filling into microcavities at the preceding and succeeding ends of the imprinting mold. Different patterns of imprinting mold were considered to enhance the fidelity of R2R-UV imprinting for the comprehensive analysis. The experimental results validated through numerical simulations revealed that the bubble entrapment can be controlled by varying various parameters such as speed of the imprinting system, viscosity, contact angles, and pattern shape. The proposed model may be useful for a continuous bubble-free R2R imprinting process in industrial applications that includes flexible displays and micro/nano-optics.