With the rapid development of high-speed rail (HSR) systems in China, the evaluation of the accessibility of HSR has become an important issue, especially for daily accessibility, or daytime round-trip travel (one-way journeys taking within 4 h), as this form of travel has significantly redefined the concept of the business trips are. This paper presents an improved approach to measuring potential-based accessibility by adding train frequency as an important weight and distinguishing the travel time into different intervals to measure accessibility. With a case study of Shandong Province, China, the paper verifies that the improved approach is more suitable for evaluating the daily accessibility and more practical for regional and transport planning than the original approach. First, the method is more effective in analyzing the differences in accessibility between cities and revealing more detailed changes or improvements in accessibility resulting from HSR. Second, there is a stronger correlation between the accessibility of different time intervals and the local economic level (GDP). Third, the method is more in line with the actual conditions in explaining the improved accessibility and corresponding spatial structures of a region. As a result, the improved approach provides an improved ability to better characterize the impacts of accessibility on regional development and will play an important role in regional planning and transportation planning. Finally, the paper also notes that the proposed approach is primarily suited for the middle-or macrolevel accessibility studies.