Quick sort algorithm has been widely used in data processing systems, because of its high efficiency, fast speed, scientific structure. Therefore, thorough study based on time complexity of quick sort algorithm is of great significance. Especially on time complexity aspect, the comparison of quick sort algorithm and other algorithm is particularly important. This paper talks about time complexity of quick sort algorithm and makes a comparison between the improved bubble sort and quick sort through analyzing the first order derivative of the function that is founded to correlate quick sort with other sorting algorithm. The comparison can promote programmers make the right decision when they face the choice of sort algorithms in a variety of circumstances so as to reduce the code size and improve efficiency of application program.