Abstract: The traditional level set method overcomes the defect that it cannot automatically create holes by arranging a certain number of holes in the initial design，but the distribution form of holes causes a strong dependency on the initial design． The improved parameterized level set method could automatically create holes，but the initial design still affected the optimization results． The level set band method can combine the level set method with the variable density method and introduce a level set band region near the zero level set，and the material density in this region was interpolated by the level set function． The intermediate density materials were gradually removed through gradually reducing the width of the level set band in the iterative process，so that the structure finally converged to a 0-1 solution． Introducing level set band can improve the continuity of objective function and constraint function in topology change by combining variable density method，so as to reduce the influence of initial design on optimization results． The compliance minimization problem proves that this method can effectively reduce the initial design dependency of the optimization results and get a better objective function value． Furthermore，the influence of the reduction speed of the width of the level set band on the optimization results was studied，and this method was extended to the optimization problem with irregular design domain and reasonable optimization results were obtained

Key words: the level set method, initial design, level set band, irregular design domain