In this letter, a compact memristor structure unit is applied for constructing the discrete chaotic system and, consequently, a memristor-type chaotic mapping is designed. Two independent system parameters are proven to be partial and total amplitude controllers. Meanwhile, the internal memristor parameter returns the map a typical bifurcation. Finally, a hardware experiment based on STM32 is carried out by verifying the theoretical finding. To the best of our knowledge, the memristor-type chaotic mapping has not been previously reported.