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Heart rate asymmetry (HRA) can investigate the asymmetric characteristics that cannot be analyzed by traditional heart rate variability (HRV). The asymmetric pattern of heart rate acceleration and deceleration can be described by the projection of RR interval (RRI) series on the Poincaré plot. In this study, two new asymmetric variables of HRA are proposed. By using the moving window method, the dynamical analysis of HRA can be illustrated on the time series diagram. Two kinds of physiological experiments and an artificial chaotic RRI system are evaluated. The binomial experimental results (p-value: 0.004) verify that the proposed method can quickly and effectively respond to the HRA.