Voltage source converter-based multi-terminal HVDC (VSC-MTDC) system has been considered for interconnecting asynchronous power grids for improved system operation efficiency and reliability. In this study, a frequency response control strategy is proposed for the VSC-MTDC systems that can enable operating reserves sharing among the interconnected asynchronous grids. The proposed control strategy consists of three frequency control components: MTDC primary frequency control, corrective frequency control, and MTDC secondary frequency control. The MTDC primary frequency control could keep the frequency of a disturbed power grid stable and avoid the frequency dropping into an unacceptable level when a sudden power imbalance event occurs. The corrective frequency control strives to guarantee the settled frequency can be within the predefined secure frequency range. The MTDC secondary frequency control provides a novel optimal allocation strategy for considering the participation of MTDC system for restoring system frequency back to the nominal frequency with the lowest cost. The simulation results, based on a modified IEEE New England 39-bus system modelled in PSCAD/EMTDC, show the effectiveness of the proposed frequency response control strategies.