In this brief, we present an adaptive framework for constructing a frequency-limited pseudo-optimal reduced-order model for the frequency-limited H2-model order reduction problem. We show that the recently developed cumulative reduction framework for moment matching, i.e., reference , can be generalized with some slight modifications for the frequency-limited model reduction scenario. The proposed algorithm adaptively increases the order of reduced model such that the frequency-limited H2-norm error decays monotonically irrespective of the choice of interpolation points and tangential directions. Moreover, it also generates the approximations of the frequency-limited system Gramians, which monotonically approach the original solution irrespective of the choice of interpolation points and tangential directions. We consider two numerical examples to validate the theory presented in the paper.