A multi-terminal hybrid high voltage direct current (HVDC) system integrating both line commutated converter (LCC) and modular multilevel converter (MMC) is becoming an emerging solution for long distance and bulk power transmission. To protect this system from short circuits, the pole-to-ground (PTG) fault current calculation is of vital importance. However, PTG fault analysis faces three major challenges: nonlinear characteristics introduced by LCC, asymmetry of PTG fault and inherent coupling between DC transmission lines. In this paper, in light of the nonlinear obstacle, DC characteristics of LCC and its specific nonlinear form are analyzed. Then, for system-level fault current calculation, a linear transient model is established for LCC with the piecewise linearization method. To address the asymmetry and coupling issues, a common- and differential-mode (CDM) transformation-based analysis method is proposed. By transforming the multi-terminal hybrid HVDC system into CDM networks, analytical expressions of PTG fault currents are presented in this paper. Analytical expression of PTG fault current reveals the underlying fault mechanism, and can be used to select proper fault protection equipment, the validity of which is fully verified by PSCAD/EMTDC simulation.