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Printing electronic components by screen printing with its excellent printing quality, high efficiency, and green environmental protection have broad application prospects in additive manufacturing. However, efficiency and quality of printing were decreased as conductive-ink blocking screen in the actual process of printing. Thus, it is pivotal that exploring factors of adhesion from the interaction of conductive-ink and screen. Herein, the functional relationship between adhesion and factors of adhesion and influence trend of adhesion on ink residue was obtained via the establishment of liquid-bridge adhesion model between two plates according to screen printing ink transfer process, solid-liquid wetting theory, and adhesion mechanism, which was verified by software Fluent. In order to justify the accuracy of the model and simulation, the adhesion and ink residue were tested on the surface-modified glass sheet as the result that the model and simulation were consistent with the experimental record. It was demonstrated that solid-liquid contact angle, tensile distance, and liquid volume are the main factors affecting the change of solid-liquid adhesion. With the increase of tensile distance and contact angle, the adhesion force decreases, which causes the decline of the residual amount of liquid on the solid surface. By means of screen modification, the adhesion between conductive-ink and screen can be reduced, as meanwhile the efficiency and quality of printed products can be improved.