External wrench estimation has become a necessary part in many emerging applications of the Unmanned Aerial Vehicles (UAVs) such as aerial contact tasks, tactile mapping and human-UAV interaction, etc. Since measurement noises of sensors may be unknown or time-varying, this letter proposes a novel external wrench estimator based on variational Bayesian unscented Kalman Filter (VBUKF). The VB algorithm is combined into an UKF based estimator for estimating the external wrench and unknown measurement noise covariance simultaneously. Simulations and actual experiments are conducted to verify the proposed method. The results demonstrate that the VBUKF based estimator is robust to unknown and changing measurement noise. It has a good precision of external wrench estimation, which is consistent with the force sensor.