Plant viral infections are primarily propagated by adult insect vectors, which generally require a maturation period of approximately ten to twelve days. Following ingestion of the virus from an infected host plant, these vectors become capable of transmitting the pathogen to susceptible plants. In this study, a stage-structured mathematical model was formulated and analyzed to characterize the transmission dynamics of plant viral diseases mediated by adult insect vectors. Particular emphasis was placed on assessing how the maturation period of vectors influences the progression of infection transmission. To establish the mathematical validity of the model, it was shown to possess non-negative and bounded solutions, which confirms its well-posedness. We identified all steady states and studied their stability. The results show how infection rate, maturation rate, and maturation time can cause stability changes in steady states. Numerical stability and simulations were presented to analyze the behaviors of the system in different dynamical regimes. The stabilizing effect of the maturation period can help develop control methods for the management of plant viral diseases.