Abstract: The paper studies the probability distribution of the first-passage time Tf of Markov process, whose times and states are both continuous. Considering minute time increment at time t, the paper examines the probability variation in the minute time-interval to find the internal relation between transition probability distribution function and first-passage times probability distribution. Finally the explicit expression of probability density function of first-passage time is obtained. The responses of linear system have Markov property under common random loads-flat noise, and the non-Markov responses process can be converted to one-dimensional Markov process by quite a few existing practical methods, so this study has generality.