In this paper, we consider the direction-of-arrival (DOA) estimation problem under fluctuating misorientation via acoustic vector sensor array (AVSA). A covariance matrix focusing fitting (CMFF) method is proposed to tackle this issue. Firstly, a new AVSA data model is created by incorporating the fluctuation parameter into different time segments. Then, to overcome the deterioration of DOA estimation performance under fluctuating misorientation in the total observation time, a covariance matrix focusing technique is formulated. By using the covariance matrix focusing technique, different time segments with fluctuating misorientation are converted into the desired data sets. Finally, to obtain more accurate DOA estimation performance, an iterative weighted covariance matrix fitting method is presented. Simulation and experimental results are carried out to demonstrate the superiority and robustness of our proposed method in the case of fluctuating misorientation for an AVSA.