Envision a ubiquitously device-free motion sensing, this work focuses on the analysis of Wi-Fi-based hand gesture trajectory tracking by utilizing Doppler frequency obtained from channel state information (CSI). Since a movement of human limb generates variant Micro-Doppler signatures caused by different parts on hand and arm surfaces to the spectrum, the estimation technique is proposed to extract the temporal profile of the hand-only Doppler signature. With a set of Doppler profiles from different pairs of Wi-Fi antenna, hand trajectory can be traced by exploiting the multi-static Doppler radar model. Kalman filter (KF) was applied to mitigate the accumulated noise from the recursive process of trajectory estimation. For the validation of the proposed method, the human limb model was developed to simulate a deterministic movement of hand gesture by exploiting the non-rigid motion of the robotic arm. The electromagnetic wave scattered from the human limb model was computed using physical optics (PO) approximation to simulate time-variant CSI. Through the experiment, hand Doppler signature could be successfully extracted from the spectrum with the error less than 4-Hz at 90 th percentile of CDF. With the extracted profiles, the trajectory of a square and M-shape gesture were successfully traced albeit a moderate trajectory offset of 10-20 degrees. The measurement conducted in the meeting room with commodity Wi-Fi devices installed on laptops also confirmed the tracking capability of the proposal. INDEX TERMS channel state information, micro-Doppler, motion sensing, non-rigid motion, trajectory tracking, Wi-Fi.