Falling in elderly is a worldwide major problem and it can lead to severe injuries or death. Despite the effort made to ensure home environments safe and foster healthy lifestyles, it is still necessary to provide methodologies that can be used at home for detect risk factors associated with falls. In this study, we proposed a new simple non-linear model, i.e., Linear-Sigmoidal model (LS), easy to fit and simple to interpret, used to model accelerometer features and outcome of the clinical scale Tinetti (clinical scale for fall risk prediction). Also, subjects with a score ≤ 18 were considered as high risk of falling. One-hundred-twelve subjects underwent to a Tinetti test while wearing a 3D axis accelerometer at the chest, and the Tinetti score used as gold standard. Ninety subjects were used as training set and twenty-two ones were employed to test the model. The same sets were used to assess the performance of the standard linear regression (LR). Seven accelerometer features and the body mass index were used in the model regression. LS resulted better than LR in terms of model agreement (R2: 0.76 vs 0.72) and classification accuracy (0.91 vs 0.86) on the test set.