An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon＇s path-integral expression of the reduced density matrix, is used to describe the exact dynamics at any dissipative strength and for arbitrarily low temperatures. The utility of the method is demonstrated by applications to a damped harmonic oscillator and a double-well system immersed in an Ohmic bath at low temperatures.