A novel, rapid algorithm to speed up and improve the reconstruction of sensitivity encoding (SENSE) MRI was proposed in this paper. The essence of the algorithm was that it iteratively solved the model of simple SENSE on a pixel-by-pixel basis in the region of support (ROS). The ROS was obtained from scout images of eight channels by morphological operations such as opening and filling. All the pixels in the FOV were paired and classified into four types, according to their spatial locations with respect to the ROS, and each with corresponding procedures of solving the inverse problem for image reconstruction. The sensitivity maps, used for the image reconstruction and covering only the ROS, were obtained by a polynomial regression model without extrapolation to keep the estimation errors small. The experiments demonstrate that the proposed method improves the reconstruction of SENSE in terms of speed and accuracy. The mean square errors (MSE) of our reconstruction is reduced by 16.05% for a 2D brain MR image and the mean MSE over the whole slices in a 3D brain MRI is reduced by 30.44% compared to those of the traditional methods. The computation time is only 25%, 45%, and 70% of the traditional method for images with numbers of pixels in the orders of 10(3), 10(4), and 10(5)-10(7), respectively.