Abstract: CSAMT is characterized by time-consuming calculation and low accuracy. The conventional inversion method has simple boundary processing, needs big memory, it is difficult to have accurate search direction, influencing severely the effect of inversion. In order to achieve rapid and high-precision forward modeling of CSAMT, to improve the boundary processing method, to reduce memory usage, to optimize the searching direction to reduce the times of iterative inversion, LBFGS CSAMT 1D inversion method based on boundary constraint and limited memory was proposed. Firstly in CSAMT forward modeling, double-precision and parallel algorithm was adopted, realizing rapid and high-precision calculation of the horizontal electric field excited by a wire source with limited length under conditions of 1D medium model. Secondly in inversion method two objective functions based on the relative error and the absolute error were constructed respectively. The constraints of smooth model were introduced. Self-adaptive regularization strategy was adopted to renewal the regularization factors. LBFGS-B algorithm of limited memory based on boundary constraint was adopted. 1D precise and rapid inversion of CSAMT was realized. The amplitude of the horizontal electric field E_x of the geoelectric model of multiple thin layers with low and high resistivity was used as inversion data to conduct direct inversion and model test. The results illustrate that this method can reflect the trend of the variation of formation resistivity with depth, and has higher resolution for thin layers with high and low resistivity, the resolving effect is better for a thin layer with low resistivity. The resolution of the inversion profile of the actual CSAMT data is superior to that of the conventional inversion method for continuous medium. The geological effect is evident, indicating that this method has good application prospect.