This paper is for enhancing the breakdown voltage of MHEMTs with an InP-etchstop layer. Gate-recess structures has been simulated and analyzed for the breakdown of the devices with the InP-etchstop layer. The fully removed recess structure in the drain side of MHEMT shows that the breakdown voltage enhances from 2V to almost 4V and that the saturation current at gate voltage of 0V is reduced from 90mA to 60mA at drain voltage of 2V. This is because the electron-captured negatively fixed charges at the drain-side interface between the InAlAs barrier layer and the $Si_3N_4$ passivation layer deplete the InGaAs channel layer more and thus decreases the electron current passing the channel layer. In the paper, the fully-recessed asymmetric gate-recess structure at the drain side shows the on-breakdown voltage enhancement from 2V to 4V in the MHEMTs.