Simultaneous perturbation stochastic approximation (SPSA) algorithm, an algorithm without secondary path modeling, has been applied to active noise control by some researchers. Some extended versions of this algorithm have been also developed to improve its performance. However, these existing algorithms are mostly dedicated to controlling the periodic noise instead of the broadband noise. In particular, background noise is not taken into account when SPSA algorithms are applied to control broadband noise. In this paper, an algorithm combining the cost function with the SPSA algorithm to control broadband noise has been proposed. The suggested cost function is an inner product of the estimated cross-correlation function between a reference vector and the error signal. The elements of the reference vector are composed of the reference signals at different times. Moreover, the algorithm analysis is performed and the numerical simulations are carried out to demonstrate the validity of the proposed algorithm. The results illustrate that the proposed algorithm can effectively reduce broadband noise when interference noise exists in the control system. Furthermore, the proposed algorithm has better convergence performance than other SPSA algorithms.