The interior point path-following method was applied to lower bound finite element limit analysis of the nonlinear programming problem. By applying the subiterative process in the Newton algorithm to solving nonlinear equations, the data storage format and solver of the displacement-based finite element method can be used directly, and large amounts of calculation can be performed element by element. The improved algorithm can be simply implemented with the existing displacement-based finite element program. An example shows that the subiteration algorithm can obtain high efficiency and precision.