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Available convergence analyses of adaptive active noise control systems apply to only theoretical cases with broad-band white noise or pure delay secondary paths. In order to investigate convergence behaviors of these systems in more practical conditions, this paper conducts a new convergence analysis for filtered-x LMS-based active noise control systems with band-limited white noise and moving average secondary paths. A linear model for the adaptation process is developed. Based on this model, the upper-bound of the adaptation step-size is derived. Also, the adaptation step-size leading to the fastest convergence rate is derived. In addition to the computer simulation, a fully implemented real time active noise control system is used to verify the validity of the analytical results.