Heart rate variability (HRV) offers a noninvasive way to peek into the physiological status of the human body. When this physiological status is dynamic, traditional HRV indices calculated from power spectrum do not resolve the dynamic situation due to the issue of nonstationarity. Clinical anesthesia is a typically dynamic situation that calls for time-varying HRV analysis. Concentration of frequency and time (ConceFT) is a nonlinear time-frequency (TF) analysis generalizing the multitaper technique and the synchrosqueezing transform. The result is a sharp TF representation capturing the dynamics inside HRV. Companion indices of the commonly applied HRV indices, including time-varying low-frequency power (tvLF), time-varying high-frequency power, and time-varying low-high ratio, are considered as measures of noxious stimulation.To evaluate the feasibility of the proposed indices, we apply these indices to study two different types of noxious stimulation, the endotracheal intubation and surgical skin incision, under general anesthesia. The performance was compared with traditional HRV indices, the heart rate reading, and indices from electroencephalography.The results indicate that the tvLF index performs best and outperforms not only the traditional HRV index, but also the commonly used heart rate reading.With the help of ConceFT, the proposed HRV indices are potential to provide a better quantification of the dynamic change of the autonomic nerve system.Our proposed scheme of time-varying HRV analysis could contribute to the clinical assessment of analgesia under general anesthesia.