Vehicle detection in aerial images is a challenging task. The complexity of the background information and the redundancy of the detection area are the main obstacles that limit the successful operation of vehicle detection based on anchors in very-high-resolution (VHR) remote sensing images. In this paper, an anchor-free target detection method is proposed to solve the problems above. First, a multi-attention feature pyramid network (MA-FPN) was designed to address the influence of noise and background information on vehicle target detection by fusing attention information in the feature pyramid network (FPN) structure. Second, a more precise foveal area (MPFA) is proposed to provide better ground truth for the anchor-free method by determining a more accurate positive sample selection area. The proposed anchor-free model with MA-FPN and MPFA can predict vehicles accurately and quickly in VHR remote sensing images through direct regression and predict the pixels in the feature map. A detailed evaluation based on remote sensing image (RSI) and vehicle detection in aerial imagery (VEDAI) data sets for vehicle detection shows that our detection method performs well, the network is simple, and the detection is fast.