The photoluminescence (PL) spectra of CdTe/Cd1-xMnxTe: In strained layer multiple quantum wells, which were prepared by MBE, are reported. A strong enhancement of the photoluminescence intensity towards the electron Fermi energys which is caused by multiple electron-hole scattering processes,and a strong asymmetry of the PL peak were observed. The physical mechanism of the Fermi edge singularity is analyzed and discussed. The photomodulation (PR) spectrum of the sample at 77K was measured and the PR spectral results, considering the PL spectra together,give further support to the discussions. In addition, the temperature dependence of the Fermi-edge singularity was measured and the results show that the Fermi-edge singularity is much stronger than that in III-V semiconductors.