Line commutated converter based high-voltage direct-current (LCC-HVDC) transmissions are prone to harmonic oscillation under weak grids. Impedance modeling is an effective method for assessing interaction stability. Firstly, this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space (HSS) model of an LCC-HVDC. Based on the HSS model, the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified. The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system. The effects of the grid strength and control parameters on system stability are also analyzed. To improve the impedance characteristics and operating stability of the LCC-HVDC system, a virtual impedance based stability enhancement control is proposed, and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends. Finally, simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.