This paper presents a VLSI-oriented arithmetic design method using a radix-2 redundant number representation with digit set {0, 1, 2} and multiple-valued current-mode (MVCM) circuit technology. We propose a carry-propagation-free (CPF) parallel addition method with redundant digit set {0, 1, 2} which is suitable for the design with MVCM circuits. Several types of CPF parallel adders are compared and the proposed CPF parallel adder with MVCM circuits offers the best total performance with respect to speed, complexity, and power dissipation. The designed basic arithmetic circuits has sufficient noise immunity to the supply voltage fluctuation which is important for stable operations of the VLSI circuits. The CPF parallel adder is effectively used as the reduction scheme of partial products in a high-speed compact multiplier. For example, the designed 3232 bit multiplier reduces the number of active elements to two-third and the number of interconnections to one-fifth of the corresponding binary Wallace tree multiplier, where the speed is almost the same. The structure is simple and regular. The static power dissipation of the designed 32-bit multiplier is estimated to be the mean value of 212 mW and the worst case of 708 mW. The total power including dynamic power dissipation would not be so large compared with that of the 32-bit binary CMOS multiplier reported under 10 MHz operation.