In this paper the short-circuit current of overhead transmission lines is analyzed at a short circuit in an HVDC transmission network. The analysis focuses solely on the current contribution of the transmission line at a line-to-earth or a line-to-line short circuit. In this context it is shown which impedance is effective at the corresponding fault case. Special attention is given to the frequency dependence of the line parameters and how they affect the short-circuit current. The frequency of the current is derived with a simplified method. Finally, it is presented how the resulting time course of the short-circuit current can be determined based on travelling wave theory. The analysis covers different HVDC grid topologies.