An on-the-fly filtered propagator functional path integral scheme is introduced as an efficient way of calculating the iterative dynamics of complex condensed systems. Time evolution of the reduced density matrix of a dissipative quantum system is evaluated iteratively by filtering the negligible propagator elements at each propagation step. This on-the-fly filtering along with the finiteness of the bath memory dramatically reduces the configuration space to be integrated without losing numerical accuracy of the results. The required computational storage space for the configuration and the weight of the survived path segments increases linearly with the bath memory length. Up to the bath memory time, it is found that a strikingly small fraction of the configurations survives the on-the-fly filtering process and the number of surviving configurations increases algebraically with the propagation time. At times longer than the bath memory time, the number of surviving configurations required for numerically accurate results is essentially saturated and is less than 0.1% of the total number of the configurations. This new scheme is extremely useful for the problems of low-frequency solvents for which the bath memory spans many time steps of the propagation.