The n-type InGaAs∕AlxGa1−xAs quantum well infrared photodetector (QWIP) with asymmetric graded barriers for broadband detection has been investigated theoretically based on the eight-band k∙p model. It is found that the intersubband transitions from the ground state to all bound and continuum excited states contribute to the overall absorption and the bound-to-continuum (B-to-C) transitions dominate. The superposition of the bound-to-bound and B-to-C transitions results in a broad detection bandwidth, and both the detected wavelength and bandwidth can be tuned by the applied voltage. The analysis method is also applicable to the GaAs∕InxGa1−xAs∕InyGa1−yAs QWIP with step quantum wells. The calculated results are consistent with the reported experimental observations.