The common way to isolate the line fault in line-commutated converter-based high-voltage direct current (LCC-HVDC) transmission grids is regulating the trigger angle of converters on both terminals of the faulted line, which usually depends entirely on the conventional controller and goes with large current peak and lengthy overcurrent duration. In this study, a trigger-angle setting approach with adaptability is, therefore, proposed to provide a theoretical basis for the generation of fault isolation strategies under different scenarios. First, equivalent circuits of solid pole-to-ground line faults at rectifier and inverter terminals are established, and time-domain expressions of the fault and converter currents are obtained. Secondly, based on the analysis of current characteristics, the non-linear programming method is utilised to obtain the optimal trigger-angle sequence after the fault, which can be applied in the following fault isolation. Finally, the proposed approach is verified via power systems computer aided design (PSCAD)/electromagnetic transients including DC (EMTDC) simulation. The results show that it can effectively reduce the current peak and the overcurrent duration of the converter, which is of positive significance for maintaining the power system security and stability.