This work is motivated by the analysis of accelerometer data. The analysis of such data consists in extracting statistics which characterize the physical activity of a subject (e.g., the mean time spent at different activity levels and the probability of the transition between two levels). Therefore , we introduce a finite mixture model of hidden Markov chain to analyze accelerometer data by considering heterogeneity into the population. This approach does not specify activity levels in advance but estimates them from the data. In addition, it allows for the heterogeneity of the population to be taken into account and defines subpopulations having a homogeneous behavior regarding the physical activity. The main theoretical result is that, under mild assumptions, the probability of misclassifying an observation decreases at an exponential rate with its length. Moreover , we prove the model identifiability and we show how the model can handle missing values. Our proposition is illustrated using real data.