This paper proposes a novel current-mode multiplier without additional carry propagation and amplification circuits. The basic functional block is a one-transistor-multi-memristor (1TxM) cell, corresponding to a partial product term. In this cell, the transistor enables or disables the term by switching it ON or OFF, and the memristor acts as the resistive memory unit that determines the state of the cell: either high (i.e. logic 0) or low (i.e. logic 1).