In some recent applications involving large-scale data analytics, a plurality of data streams are sequentially observed in parallel, and the statistical decision maker is asked to screen out among these data streams those that exhibit certain characteristics. Motivated by such setting, in this work, a parallel sequential change detection model is investigated. In the model, a plurality of independent parallel data streams, each of which has a change-point with a certain prior probability distribution, are sequentially observed with a maximum sampling constraint. A sequential procedure is developed to inspect these parallel data streams and to decide, for each of them, whether a change has occurred. The sequential procedure is shown to guarantee the false discovery rate (FDR). The average detection delay over the parallel data streams is also quantified in asymptotic regimes. Numerical experiments are conducted to illustrate the proposed sequential procedure.