It is a challenging task to handle the vector field visualization at  local critical points. Generally, topological based methods firstly divide critical regions into different categories, and then process the different types of critical regions to improve the effect, which pipeline is complex. In the paper, a learning based multi-task super resolution (SR) method is proposed to improve the refinement of vector field, and enhance the visualization effect, especially at the critical region. In detail, the multi-task model consists of two important des igns on task branches: one task is to simulate the interpolation of discrete vector fields based on an improved super-resolution network; and the other is a classification task to identify the types of critical vector fields. It is an efficient end-to-end architecture for both training and inferencing stages, which simplifies the pipeline of critical vector field visualization and improves the visualization effect. In experiment, we compare our method with both traditional interpolation and pure SR network on both simulation data and real data, and the reported results indicate our method lower the error and improve PSNR significantly.