Gas turbine maintenance strategy relies heavily on accurate estimation of critical component life consumption of gas turbine engines during their operations. The equivalent operating hours (EOH) is a useful concept to measure the engine life consumption and support condition-based maintenance planning for gas turbine engines and their critical components. However, the current EOH calculation methods are mostly empirical and engine-specific, relying on vast operating data and experience. This paper introduces a novel physics-based method to estimate the EOH of the high-pressure turbine rotor blades of a gas turbine engine based on the damages caused by creep and low-cycle fatigue (creep-LCF) interactions. The method has been applied to a typical turbofan engine taking both 440-minute long-haul flight at one flight per day and 60-minute short-haul flight at two flights per day. A comparison of the predicted damages and life consumptions indicates that the creep EOH and also the creep damage of the engine of the short-haul aircraft is about 1.38 times that of the engine of the long-haul aircraft, the LCF equivalent operating cycles (EOC) and also the LCF damage of the engine of the short-haul aircraft is about 2.0 times that of the engine of the long-haul aircraft, and the total damages are more affected by the creep damage than the LCF damage with the creep damage being 6.78 times the LCF damage for the engine of the short-haul aircraft and 9.81 times for the engine of the long-haul aircraft. In addition, the total EOH or the total damage of the engine of the short-haul aircraft is about 1.44 times that of the engine of the long-haul aircraft. The proposed method shows a great potential to provide a quick estimate of the life consumption of gas turbine engines for condition monitoring, and it can be applied to other types of gas turbine engines.