In this paper, we analyze current-voltage characteristics of InSb/AlInSb triple-barrier resonant tunneling diodes (TBRTDs) with spin-splitting under zero magnetic fields. The InSb has very small effective mass, thus we can obtain large spin-splitting by Rashba spin-orbit interaction due to asymmetric InSb/AlInSb quantum wells. In our model, broadening of each resonant tunneling level and spin-splitting energy can be considered to calculate spin-polarized resonant tunneling current.