Driving cycle (DC) plays an important role in designing and evaluating EVs, and many Markov chain-based DC construction methods describe driving profiles of unfixed-line vehicles with Markov state transition probability. However, for fixed-line electric vehicles, the time-sequence of microtrips brings huge influences on their brake, drive, and battery management systems. Simply describing topography, traffic, location, driving features, and environment in a stochastic manner cannot reflect the continuity characteristics hidden in a fixed route. Thus, in this paper, we propose a sticky sampling and Markov state transition matrix based DC construction algorithm to describe both randomness and continuity hidden in a fixed route, in which a data structure named “driving pulse chain” was constructed to describe the sequence of the driving scenarios and several Markov state transition matrices were constructed to describe the random distribution of velocity and acceleration in same driving scenarios. Simulation and experimental analysis show that with sliding window and driving pulse chain, the proposed algorithm can describe and reflect the continuity characteristics of topography, traffic, and location. At the same time, the stochastic nature of the driving cycle can be preserved.