The average police salary at City of Graham was $42,278 , which is 36 percent lower than the average salary for this job in Texas, and 50 percent lower than the national average for this job . Police salaries at City of Graham typically range from $18,264 to $63,341 (25th to 75th percentile). The highest reported police salary was $69,435. There are 19 employees at City of Graham with the job title police.