: New nanotechnology based devices are replacing CMOS devices to overcome CMOS technology’s scaling limitations. However, many such devices exhibit nonmonotonic I-V characteristics and uncertain properties which lead to the negative differential resistance (NDR) problem and the chaotic performance. This paper proposes a new circuit simulation approach that can effectively simulate nanotechnology devices with uncertain input sources and negative differential resistance (NDR) problem. The experimental results show a 20-30 times speedup comparing with existing simulators.