This study proposes a maximum-likelihood-estimation method for a quadrotor UAV given the existence of sensor delays. The state equation of the UAV is nonlinear, and thus, we propose an approximated method that consists of two steps. The first step estimates the past state based on the delayed output through an extended Kalman filter. The second step involves calculating an estimate of the present state by simulating the original system from the past to the present. It is proven that the proposed method provides an approximated maximum-likelihood-estimation. The effectiveness of the estimator is verified by performing experiments.