In one embodiment, a processor includes: at least one core; and a power controller coupled to the at least one core. The power controller may include: a workload monitor circuit to calculate a background task ratio based on a first amount of time that the at least one core executed background tasks during an active duration; and a control circuit to dynamically apply a power management policy for a background mode when the background task ratio exceeds a background mode threshold, the power management policy for the background mode to reduce power consumption of the processor. Other embodiments are described and claimed.