In this work, we have modelled and computed the transport properties of the double-barrier InGaAs/GaAsSb structure from the resonant tunnelling point of view. Based on the classical Tsu-Esaki formula for the tunnelling current, we have calculated the current density-voltage characteristic of a Al-free type-II hbox {In}_{0.53}hbox {Ga}_{0.47}hbox {As/GaAs}_{0.51}hbox {Sb}_{0.49} structure at different cryogenic and elevated temperatures. The tunnelling coefficient has been calculated in the framework of effective mass approximation with nonparabolicity included, using the transfer matrix approach. A good qualitative agreement of the position of resonant current peaks with the existing experimental data was achieved. Our calculation shows a very high sensitivity of the tunnelling current peak on monolayer-scale layer structure fluctuation which strongly affects peak to valley ratio in the resonant tunnelling structure.