Experimental and modelling study of the pre-breakdown phenomenon in dielectric liquids, generally called 'streamers', is vital for the application of liquids in high voltage and power dense devices. Streamer is characterized into four modes by average propagation velocity, among which the second mode streamer is responsible for breakdowns at a wide range of gap distances and voltage levels. The stable propagation velocity of around 2 km s-1 is one of the key characteristics of the second mode streamer. The most recent study found that streamer branching is not the main reason for the stable velocity of second mode streamer as was assumed previously. Besides, one major drawback of the existing charge-drift model of the second mode streamer is the over-estimation of electron velocity, which leads to the much higher streamer propagation velocity in simulation than that observed in experiments. In this paper, restriction of streamer propagaiton velocity by using electron saturation velocity (ESV) is found to be the key reason for the stable propagaiton velocity of the second mode streamer. The charge-drift model is modified by considering different ESVs. It is found that reducing ESV from 30 km s-1 to 2.5 km s-1 in simulation can greatly constrain positive streamer propagation velocity from 4.15 km s-1 to 0.50 km s-1 in cyclohexane. When ESV is set to be 7.5 km s-1 in cyclohexane, the streamer propagation velocity in simulation increases from 1.59 km s-1 at 80 kV (below breakdown voltage) to 1.91 km s-1 at 100 kV (near to acceleration voltage), which closely matches the experimental observations.