High Voltage Direct Current (HVDC) technology based on line commutated converters (LCC) is crucial for integrating large-scale renewable energy and long-distance power transmission. However, high-frequency oscillations in the HVDC system can significantly hinder transmission capacity and grid safety. it is necessary to establish a dynamic mathematical model that can accurately evaluate its harmonic current. Taking the LCC-HVDC controlled by typical voltage loop and current loop as the object, a dynamic mathematical model that can accurately reflect the grid-connected harmonic current of LCC-HVDC is established by comprehensively considering the influence of background harmonics and modulation. Finally, the accuracy of the dynamic mathematical model established in the article was verified by comparing the calculation data of LCC-HVDC with the simulation data, and the influence of control factors and short-circuit ratio on harmonic current was analyzed. This provides a means and basis for the quantitative analysis and evaluation of LCC-HVDC grid connected harmonic currents.