The average City of Graham police salary was $42,278, which is 49 percent lower than the average salary for this job in Texas, and 45 percent lower then the average salary for this job nationwide. Police salary in City of Graham is usually between $18,264 and $63,341 (25th and 75th). The highest police salary in City of Graham was $69,435. There are 19 employees in City of Graham whose job title is police.