We present an adaptive autofocusing scheme. In this scheme, the focus measure is updated with focus tuning. To achieve this, we construct the focus measure by using image moments and develop an adaptive focus-tuning strategy to estimate the measure in closed loop. It is shown that the adaptive updating of the focus measure enables us to overcome the dependence of autofocusing on the image contents. Such an adaptive closed-loop focusing operation also effectively suppresses both the effect of the noise in optical imaging and the effect of time delay due to image processing time. Therefore a high accuracy of autofocusing is guaranteed. The effectiveness of the proposed scheme is demonstrated by simulations and experiments.