We present theoretical calculation of the absorption between the conduction subbands in a modulation-doped $Al_xGa_{1-x}As$/GaAs superlattice. The electronic subband structures, including both the coupling between different quantum wells and the band bending due to screening effects, are calculated self-consistently the $Schr\ddot{o}dinger$ and Poisson equation. Linear intersubband absorption in the superlattice is then calculated and the absorption spectra show interesting line shapes which reflect the joint density of states between different subbands. We also investigate the dependence of the absorption(energy band width, resonant absorption energy and magnitude of peak absorption coefficient) on device parameters such as doping concentration, well width, barrier width and aluminum mole fraction in the barrier, which are useful for the design of infrared of infrared detectors. We also compare our theoretical results with experimental data and find good agreement.