Heart rate variability (HRV) analysis is a non-invasive and reliable means to assess an autonomic nervous system (ANS) function. Heart rate is a non-stationary signal that may contain indicators of current diseases and sometimes warnings about impending diseases. In this paper, we have proposed the threshold-based acceleration change index (TACI) for HRV analysis, which is calculated from the sign of differences of RR time series characterizing the dynamics of threshold crossings. It was found that TACI is robust in classifying various groups under different physiological and pathological conditions. We have studied the behavior of TACI for simulated time series (uncorrelated random data, sinusoidal time series and logistics map time series) and its robustness in the presence of artifacts for RR time series. The performance of TACI is evaluated for classifying normal sinus rhythm (NSR), congestive heart failure (CHF) and atrial fibrillation (AF). An unpaired Student\'s t-test was used to check significant differences between these groups and the degree of separation between these groups was quantified by using the area of a receiver operator curve.