In issue tracking systems, each bug is assigned a priority level (e.g., Blocker, Critical, Major, Minor, or Trivial in JIRA from highest to lowest), which indicates the urgency level of the bug. In this sense, understanding bug priority changes helps to arrange the work schedule of participants reasonably, and facilitates a better analysis and resolution of bugs. According to the data extracted from JIRA deployed by Apache, a proportion of bugs in each project underwent priority changes after such bugs were reported, which brings uncertainty to the bug fixing process. However, there is a lack of in-depth investigation on the phenomenon of bug priority changes, which may negatively impact the bug fixing process. Thus, we conducted a quantitative empirical study on bugs with priority changes through analyzing 32 non-trivial Apache open source software projects. The results show that: (1) 8.3% of the bugs in the selected projects underwent priority changes; (2) the median priority change time interval is merely a few days for most (28 out of 32) projects, and half (50. 7%) of bug priority changes occurred before bugs were handled; (3) for all selected projects, 87.9% of the bugs with priority changes underwent only one priority change, most priority changes tend to shift the priority to its adjacent priority, and a higher priority has a greater probability to undergo priority change; (4) bugs that require bug-fixing changes of higher complexity or that have more comments are likely to undergo priority changes; and (5) priorities of bugs reported or allocated by a few specific participants are more likely to be modified, and maximally only one participant in each project tends to modify priorities.