The mean firstpassage time in an asymmetric bistable system with timedelayed feedback was investigated. Under the condition of small time delay approximation theory, the approximate FokkerPlanck equation and the stationary probability distribution function were obtained, then the expression of the mean firstpassage time was obtained, and the theoretical results by numerical simulation were discussed . Numerical results show that: (1) The value of the delay time can cause different effects on the stationary probability distribution function: when,there are still two peaks in the curve of the stationary probability distribution; when,there exists a valley in the curve of the stationary probability distribution; (2) when, we studied the effects of multiplicative noise intensityand additive noise intensity on the mean firstpassage time, and found there existed a valley in the curve of  ,while the curve of  a was monotonic.