Singing voice beat and downbeat tracking posses several applications in automatic music production, analysis and manipulation. Among them, some require real-time processing, such as live performance processing and auto-accompaniment for singing inputs. This task is challenging owing to the non-trivial rhythmic and harmonic patterns in singing signals. For real-time processing, it introduces further constraints such as inaccessibility to future data and the impossibility to correct the previous results that are inconsistent with the latter ones. In this paper, we introduce the first system that tracks the beats and downbeats of singing voices in real-time. Specifically, we propose a novel dynamic particle filtering approach that incorporates offline historical data to correct the online inference by using a variable number of particles. We evaluate the performance on two datasets: GTZAN with the separated vocal tracks, and an in-house dataset with the original vocal stems. Experimental result demonstrates that our proposed approach outperforms the baseline by 3-5%.