The transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.