Existing studies have focused on gig workers' voice behavior and the mechanisms through which it is expressed via official and unofficial channels, the underlying logic of voice behavior generation, particularly its operational pathways under algorithmic control remains under-investigated. Drawing on fairness heuristic theory, this paper proposes a moderated mediation model to explore the effect of perceived algorithmic control on gig workers' voice behavior and its boundary condition. Based on the questionnaire data of 260 gig workers, the empirical results indicate that perceived algorithmic control significantly and positively predicts gig workers' voice behavior by enhancing their perception of algorithmic fairness. Furthermore, voice endorsement moderates the relationship between perception of algorithmic fairness and voice behavior. Complementing these findings, in-depth interviews with 22 gig workers provide a more nuanced understanding of how individuals construct fairness perceptions under algorithmic control and how these perceptions inform their decisions to engage in voice behavior.