The graph with maximum least eigenvalue of signless Laplacian among all the graphs in a certain class is often called maximized graph.We obtain the value of the least eigenvalue of signless Laplacian of connected graph with only one cut vertex by the way of using eigenvector equation to study eigenvalue.Furthermore,we get the maximum of least eigenvalue of signless Laplacian of all the connected graphs of the same order with only one cut vertex and depict corresponding structure of the maximizing graph with maximum of least eigenvalue of signless Laplacian.