Device-free human gesture recognition (HGR) using commercial off the shelf (COTS) Wi-Fi devices has gained attention with recent advances in wireless technology. HGR recognizes the human activity performed, by capturing the reflections of Wi-Fi signals from moving humans and storing them as raw channel state information (CSI) traces. Existing work on HGR applies noise reduction and transformation to pre-process the raw CSI traces. However, these methods fail to capture the non-Gaussian information in the raw CSI data due to its limitation to deal with linear signal representation alone. The proposed higher order statistics-based recognition (HOS-Re) model extracts higher order statistical (HOS) features from raw CSI traces and selects a robust feature subset for the recognition task. HOS-Re addresses the limitations in the existing methods, by extracting third order cumulant features that maximizes the recognition accuracy. Subsequently, feature selection methods derived from information theory construct a robust and highly informative feature subset, fed as input to the multilevel support vector machine (SVM) classifier in order to measure the performance. The proposed methodology is validated using a public database SignFi, consisting of 276 gestures with 8280 gesture instances, out of which 5520 are from the laboratory and 2760 from the home environment using a 10 × 5 cross-validation. HOS-Re achieved an average recognition accuracy of 97.84%, 98.26% and 96.34% for the lab, home and lab + home environment respectively. The average recognition accuracy for 150 sign gestures with 7500 instances, collected from five different users was 96.23% in the laboratory environment.